Graded algebras in algebraic geometry:
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin
De Gruyter
[2022]
|
| Series: | De Gruyter expositions in mathematics
volume 70 |
| Subjects: | |
| Online Access: | https://www.degruyter.com/isbn/9783110637540 Inhaltsverzeichnis Inhaltsverzeichnis |
| Physical Description: | XV, 445 Seiten 24 cm, 876 g |
| ISBN: | 9783110637540 3110637545 |
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MARC
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| 100 | 1 | |a Simis, Aron |d 1942- |e Verfasser |0 (DE-588)120670683X |4 aut | |
| 245 | 1 | 0 | |a Graded algebras in algebraic geometry |c Aron Simis, Zaqueu Ramos |
| 264 | 1 | |a Berlin |b De Gruyter |c [2022] | |
| 300 | |a XV, 445 Seiten |c 24 cm, 876 g | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a De Gruyter expositions in mathematics |v volume 70 | |
| 650 | 0 | 7 | |a Graduierter Ring |0 (DE-588)4158003-5 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Kommutative Algebra |0 (DE-588)4164821-3 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Algebraische Geometrie |0 (DE-588)4001161-6 |2 gnd |9 rswk-swf |
| 653 | |a Graduierter Modul | ||
| 653 | |a Graduierter Ring | ||
| 653 | |a Kommutative Algebra | ||
| 653 | |a Schnitt <Mathematik> | ||
| 653 | |a Algebraische Geometrie | ||
| 689 | 0 | 0 | |a Algebraische Geometrie |0 (DE-588)4001161-6 |D s |
| 689 | 0 | 1 | |a Kommutative Algebra |0 (DE-588)4164821-3 |D s |
| 689 | 0 | 2 | |a Graduierter Ring |0 (DE-588)4158003-5 |D s |
| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Ramos, Zaqueu |e Verfasser |0 (DE-588)1264231784 |4 aut | |
| 710 | 2 | |a Walter de Gruyter GmbH & Co. KG |0 (DE-588)10095502-2 |4 pbl | |
| 776 | 0 | 8 | |i Erscheint auch als |n Online-Ausgabe |a Simis, Aron, 1942- |t Graded Algebras in Algebraic Geometry |b 1. Auflage |d Berlin/Boston : De Gruyter, 2022 |h Online-Ressource, 464 Seiten |
| 776 | 0 | 8 | |i Erscheint auch als |n Online-Ausgabe |z 9783110640694 |
| 830 | 0 | |a De Gruyter expositions in mathematics |v volume 70 |w (DE-604)BV004069300 |9 70 | |
| 856 | 4 | 2 | |m X:MVB |u https://www.degruyter.com/isbn/9783110637540 |
| 856 | 4 | 2 | |m B:DE-101 |q application/pdf |u https://d-nb.info/1245021982/04 |3 Inhaltsverzeichnis |
| 856 | 4 | 2 | |m DNB Datenaustausch |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=033866510&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
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Record in the Search Index
| _version_ | 1816707099210547200 |
|---|---|
| adam_text |
CONTENTS
ACKNOWLEDGMENTS
-
VII
FOREWORD
-
IX
1
1.1
1.2
1.2.1
1.2.2
1.3
1.4
GEOMETRIC
MOTIVATION
-
1
BITS
FROM
INTERSECTION
THEORY
-
1
CORRESPONDENCES
AND
INCIDENCE
VARIETIES
-
4
EXAMPLES
----
4
ALGEBRAIC
COUNTERPART
-
6
RULED
JOINS
----
7
EXERCISES
-
10
2
2.1
2.2
2.2.1
2.2.2
2.3
2.3.1
2.3.2
2.3.3
2.3.4
2.4
GRADED
ALGEBRAS
-
13
ARBITRARY
GRADINGS
-
13
NOTABLE
BIGRADED
ALGEBRAS
-
16
THE
SYMMETRIC
ALGEBRA
-
16
OTHER
BIGRADED
ALGEBRAS
-
18
STANDARD
GRADED
ALGEBRAS
-
18
REES
ALGEBRAS
OF
IDEALS
-
18
REES
ALGEBRAS
OF
MODULES
----
28
COMPLEMENTS
ON
THE
FIBER
CONE
-
36
COHOMOLOGICAL
INVARIANTS
-
39
EXERCISES
-
41
3
3.1
3.1.1
3.1.2
3.2
3.2.1
3.2.2
3.2.3
3.2.4
3.2.5
3.3
3.3.1
3.3.2
3.4
3.4.1
3.4.2
RATIONAL
MAPS,
1
-
47
BASICS
OF
RATIONAL
MAPS
-
47
TERMINOLOGY
-
47
BASIC
PROPERTIES
-
48
A
CHARACTERISTIC-FREE
CRITERION
OF
BIRATIONALITY
-
50
PROLEGOMENA:
THE
KOSZUL-HILBERT
LEMMA
-
50
PRELIMINARIES
ON
RATIONAL
MAPS
ON
REDUCED
VARIETIES
-
51
THE
JACOBIAN
DUAL
RANK
VERSUS
BIRATIONALITY
-
59
STATEMENT
AND
PROOF
OF
THE
CRITERION
-
63
A
ROLE
OF
SYZYGIES
----
67
BIRATIONAL
COMBINATORICS
-
70
THE
UNDERLYING
ARITHMETIC
-
71
MONOMIAL
BIRATIONAL
MAPS
IN
DEGREE
TWO
-
73
ON
THE
DEGREE
OF
A
RATIONAL
MAP
-
77
BASIC
INGREDIENTS
-
77
DEGREE
UPPER
BOUNDS
-
81
XII
CONTENTS
3.5
EXERCISES
-----
85
4
RATIONAL
MAPS,
II
-
89
4.1
COMPLEMENTS
ON
THE
BASE
IDEAL
----89
4.1.1
DEGREE
SEQUENCES
-
89
4.1.2
THE
SEMILINEAR
RELATION
TYPE
------92
4.2
INVERSION
FACTORS
OF
BIRATIONAL
MAPS
----
93
4.2.1
BASIC
LANDSCAPE
----
94
4.2.2
RELATION
TO
SYMBOLIC
POWERS
-------
96
4.3
NEWTON
COMPLEMENTARY
DUAL
-------
97
4.3.1
PRELIMINARIES
----
97
4.3.2
MAIN
RESULTS
----
99
4.3.3
RELATION
TO
THE
GRAPH
OF
A
RATIONAL
MAP
----
104
4.4
ELEMENTS
OF
RATIONAL
MAPS
OVER
A
GROUND
RING
----
108
4.4.1
ALGEBRAIC
DATA
----
108
4.4.2
RATIONAL
MAPS
AND
REPRESENTATIVES
-----
110
4.4.3
DEGREE
UNDER
SPECIALIZATION
----
113
4.5
EXERCISES
----
115
5
THE
GRADIENT
IDEAL
-
119
5.1
THE
UNDERLYING
GEOMETRY
-----
119
5.1.1
LINEAR
TYPE
----
120
5.1.2
HYPERPLANE
ARRANGEMENTS
----
121
5.1.3
BEHAVIOR
ALONG
A
FAMILY
-----
129
5.2
FREE
DIVISORS
-----
140
5.2.1
GENERAL
NONSENSE
----
140
5.2.2
ALGEBRAIC
LOGARITHMIC
VECTOR
FIELDS
-----
141
5.2.3
FAMILIES
OF
FREE
DIVISORS
-----
145
5.2.4
WEIGHTED
HOMOGENEOUS
DIVISORS
----
148
5.3
EXERCISES
-----
155
6
CREMONA
TRANSFORMATIONS,
I
-
159
6.1
PLANE
CREMONA
TRANSFORMATIONS:
HOMALOIDAL
NETS
----
159
6.1.1
WEIGHTED
CLUSTER
OF
BASE
POINTS
----
159
6.1.2
RELATION
TO
FAT
IDEALS
----
163
6.1.3
FROM
FAT
IDEALS
BACK
TO
THE
CREMONA
BASE
IDEAL
-
172
6.1.4
PROPER
HOMALOIDAL
TYPES
WITH
LARGE
HIGHEST
VIRTUAL
MULTIPLICITY
----
173
6.2
PLANE
CREMONA
TRANSFORMATIONS:
SUBHOMALOIDAL
TYPES
-
179
6.2.1
ARITHMETIC
QUADRATIC
TRANSFORMATIONS
ACTING
ON
FAT
POINTS
----
179
6.2.2
SUBHOMALOIDAL
MULTIPLICITY
SETS
-----
181
6.2.3
3-UNIFORM
SUBHOMALOIDAL
TYPES
-----
183
6.2.4
MAIN
THEOREM
----
199
CONTENTS
-
XIII
6.2.5
6.3
7
7.1
7.1.1
7.1.2
7.1.3
7.1.4
7.1.5
7.2
7.2.1
7.2.2
7.2.3
7.3
7.3.1
7.3.2
7.3.3
7.4
8
8.1
8.2
8.3
8.3.1
8.3.2
8.3.3
8.4
8.4.1
8.4.2
8.5
8.6
8.7
9
9.1
9.1.1
9.1.2
9.1.3
9.2
RELATION
TO
BORDIGA-WHITE
PARAMETRIZATIONS
----
203
EXERCISES
----
206
CREMONA
TRANSFORMATIONS,
II
-
209
GENERALIZED
DE
JONQUIERES
TRANSFORMATIONS
----
209
FULLY
DOWNGRADED
SEQUENCES
-
211
GENERALIZED
DE
JONQUIERES
TRANSFORMATIONS
----
213
GENERALIZED
DE
JONQUIERES
TRANSFORMATIONS
UNDER
NEWTON
DUALITY
----
215
GENERALIZED
DE
JONQUIERES
TRANSFORMATIONS
WITH
IDENTITY
SUPPORT
----
218
THE
MINIMAL
FREE
RESOLUTION
OF
THE
BASE
IDEAL
----
218
THE
GRAPH
(BLOWUP)
OF
A
CREMONA
MAP
----
220
THE
GRAPH
OF
A
DE
JONQUIERES
MAP
WITH
IDENTITY
SUPPORT
----
220
CREMONA
MAPS
WITH
A
COHEN-MACAULAY
GRAPH
----
227
CREMONA
MAPS
AND
SYMBOLIC
REES
ALGEBRAS
-
231
MONOMIAL
CREMONA
TRANSFORMATIONS
----
235
THE
GROUP
OF
MONOMIAL
CREMONA
TRANSFORMATIONS
----
235
MONOMIAL
CREMONA
TRANSFORMATIONS
OF
DEGREE
2
----
243
A
DUALITY
PRINCIPLE
----
256
EXERCISES
----
259
STEPS
IN
ELIMINATION
-
263
ELIMINATION
ALGEBRAS
----
263
IMPLICITIZATION
----
266
DE
JONQUIERES
LIKE
IMPLICITIZATION
----
267
ALGEBRAIC
PRELIMS
----
267
THE
(/F,G)-PARAMETRIZATION
----
268
THE
EQUATIONS
OF
THE
REES
ALGEBRA
----
273
IMPLICITIZATION
IN
DIMENSION
1
----
278
DIMENSION
ZERO
----
278
DIMENSION
ONE
----
293
THE
CLASSICAL
RESULTANT
----
295
ELIMINATING
FROM
CORRESPONDENCES
----
297
EXERCISES
----
300
THE
GAUSS
MAP
-
303
GAUSS
IMAGE
OF
HIGHER
ORDER
----
303
NOTABLE
CASES.
I:
THE
ORDINARY
GAUSS
IMAGE
----
305
NOTABLE
CASES.
II:
THE
DUAL
VARIETY
----
306
RELATION
TO
THE
TANGENTIAL
VARIETY
----
308
THE
GAUSS
IMAGE
OF
A
UNIRATIONAL
VARIETY
----
310
XIV
CONTENTS
9.2.1
THE
ALGEBRAIC
STRUCTURAL
DATA
-
310
9.2.2
THE
GAUSS
IMAGE
OF
TORIC
VARIETIES
----
313
9.2.3
ALGEBRAS
OF
VERONESE
TYPE
-
314
9.3
ABSTRACT
GAUSS
MAPS
----
316
9.4
THE
GEOMETRY
OF
THE
ANALYTIC
SPREAD
----
317
9.4.1
MAXIMAL
ANALYTIC
SPREAD
-
317
9.4.2
ANALYTIC
SPREAD
VERSUS
THE
FITTING
IDEAL
----
322
9.4.3
CASE
STUDY:
THE
MODULE
OF
DIFFERENTIALS
-
323
9.4.4
MAIN
THEOREM
OF
ABSTRACT
GAUSS
MAPS
----
325
9.5
EXERCISES
-----
329
10
TANGENT
VARIETIES
----
333
10.1
ALGEBRAIC
FULTON-HANSEN
THEOREMS
-----
333
10.1.1
ALGEBRAIC
PRELIMINARIES
-
333
10.1.2
THE
UNDERLYING
GEOMETRY
----
337
10.1.3
THE
TANGENTIAL
VARIETY
TO
A
UNIRATIONAL
VARIETY
-
340
10.2
REFINED
PROPERTIES
OF
TANGENT
ALGEBRAS
-
341
10.2.1
EXPECTED
STAR
DIMENSION
----
343
10.2.2
SET
THEORETIC
STARLIKE
LINEARITY
-----
347
10.2.3
STARLIKE
LINEARITY
-
348
10.2.4
BEHAVIOR
UNDER
FLAT
DEFORMATION
-
351
10.2.5
A
GLIMPSE
OF
THE
BLOWUP
OF
THE
KAHLER
DIFFERENTIALS
----
354
10.3
EXERCISES
-----
356
11
EMBEDDED
JOINSAND
SECANTS
-
359
11.1
JOINS
----
359
11.1.1
ALGEBRAIC
SIDE
-----
359
11.1.2
THE
GEOMETRIC
BACKGROUND
-----
360
11.1.3
RELATION
TO
THE
BAYER-MUMFORD
DEFORMATION
-
363
11.1.4
THE
EMBEDDED
JOIN
OF
A
UNION
OF
LINEAR
SPACES
-
366
11.1.5
INITIAL
DEGREE
OF
A
JOIN
-
368
11.2
SECANTS
-----
369
11.2.1
SECANTS
OF
DETERMINANTALAND
PFAFFIAN
SCHEMES
-
370
11.2.2
SECANTS
OFVARIETIES
CUT
BY
QUADRICS
-
374
11.2.3
SECANT
ALGEBRAS
OF
MONOMIAL
IDEALS
-
377
11.2.4
RELATION
TO
STARLIKE
LINEARITY
-
378
11.2.5
HIGHER
SECANTS
----
380
11.3
EXCERPTS
ON
THE
DIAGONAL
IDEAL
-
381
11.3.1
SYZYGIES
AND
DIMENSION
-----
382
11.3.2
THE
LINEAR
TYPE
PROPERTY
-----
383
11.4
EXERCISES
----
386
CONTENTS
XV
12
ALUFFI
ALGEBRAS
-
389
12.1
RELATION
TO
CHERN
CLASSES
-----
389
12.2
THE
CASE
OF
IDEALS:
EMBEDDED
VERSION
----
390
12.2.1
PRELIMINARIES
----
390
12.2.2
DIMENSION
----
392
12.2.3
TORSION
AND
MINIMAL
PRIMES
-----
395
12.2.4
RELATION
TO
THE
ARTIN-REES
NUMBER
----
398
12.2.5
SELECTED
EXAMPLES
----
402
12.2.6
THE
ALUFFI
ALGEBRA
OF
A
GRADIENT
IDEAL
----
405
12.3
THE
CASE
OF
MODULES
-----
407
12.3.1
THE
EMBEDDED
VERSION
-----
408
12.3.2
TAKING
INVERSE
LIMIT
-----
409
12.3.3
THE
MODULE
OF
DERIVATIONS
OF
A
POLYNOMIAL
FORM
----
413
12.3.4
THE
NORMAL
MODULE
OF
A
PERFECT
IDEAL
OF
CODIMENSION
2
----
421
12.4
EXERCISES
----
427
BIBLIOGRAPHY----
431
INDEX
----
441 |
| adam_txt |
CONTENTS
ACKNOWLEDGMENTS
-
VII
FOREWORD
-
IX
1
1.1
1.2
1.2.1
1.2.2
1.3
1.4
GEOMETRIC
MOTIVATION
-
1
BITS
FROM
INTERSECTION
THEORY
-
1
CORRESPONDENCES
AND
INCIDENCE
VARIETIES
-
4
EXAMPLES
----
4
ALGEBRAIC
COUNTERPART
-
6
RULED
JOINS
----
7
EXERCISES
-
10
2
2.1
2.2
2.2.1
2.2.2
2.3
2.3.1
2.3.2
2.3.3
2.3.4
2.4
GRADED
ALGEBRAS
-
13
ARBITRARY
GRADINGS
-
13
NOTABLE
BIGRADED
ALGEBRAS
-
16
THE
SYMMETRIC
ALGEBRA
-
16
OTHER
BIGRADED
ALGEBRAS
-
18
STANDARD
GRADED
ALGEBRAS
-
18
REES
ALGEBRAS
OF
IDEALS
-
18
REES
ALGEBRAS
OF
MODULES
----
28
COMPLEMENTS
ON
THE
FIBER
CONE
-
36
COHOMOLOGICAL
INVARIANTS
-
39
EXERCISES
-
41
3
3.1
3.1.1
3.1.2
3.2
3.2.1
3.2.2
3.2.3
3.2.4
3.2.5
3.3
3.3.1
3.3.2
3.4
3.4.1
3.4.2
RATIONAL
MAPS,
1
-
47
BASICS
OF
RATIONAL
MAPS
-
47
TERMINOLOGY
-
47
BASIC
PROPERTIES
-
48
A
CHARACTERISTIC-FREE
CRITERION
OF
BIRATIONALITY
-
50
PROLEGOMENA:
THE
KOSZUL-HILBERT
LEMMA
-
50
PRELIMINARIES
ON
RATIONAL
MAPS
ON
REDUCED
VARIETIES
-
51
THE
JACOBIAN
DUAL
RANK
VERSUS
BIRATIONALITY
-
59
STATEMENT
AND
PROOF
OF
THE
CRITERION
-
63
A
ROLE
OF
SYZYGIES
----
67
BIRATIONAL
COMBINATORICS
-
70
THE
UNDERLYING
ARITHMETIC
-
71
MONOMIAL
BIRATIONAL
MAPS
IN
DEGREE
TWO
-
73
ON
THE
DEGREE
OF
A
RATIONAL
MAP
-
77
BASIC
INGREDIENTS
-
77
DEGREE
UPPER
BOUNDS
-
81
XII
CONTENTS
3.5
EXERCISES
-----
85
4
RATIONAL
MAPS,
II
-
89
4.1
COMPLEMENTS
ON
THE
BASE
IDEAL
----89
4.1.1
DEGREE
SEQUENCES
-
89
4.1.2
THE
SEMILINEAR
RELATION
TYPE
------92
4.2
INVERSION
FACTORS
OF
BIRATIONAL
MAPS
----
93
4.2.1
BASIC
LANDSCAPE
----
94
4.2.2
RELATION
TO
SYMBOLIC
POWERS
-------
96
4.3
NEWTON
COMPLEMENTARY
DUAL
-------
97
4.3.1
PRELIMINARIES
----
97
4.3.2
MAIN
RESULTS
----
99
4.3.3
RELATION
TO
THE
GRAPH
OF
A
RATIONAL
MAP
----
104
4.4
ELEMENTS
OF
RATIONAL
MAPS
OVER
A
GROUND
RING
----
108
4.4.1
ALGEBRAIC
DATA
----
108
4.4.2
RATIONAL
MAPS
AND
REPRESENTATIVES
-----
110
4.4.3
DEGREE
UNDER
SPECIALIZATION
----
113
4.5
EXERCISES
----
115
5
THE
GRADIENT
IDEAL
-
119
5.1
THE
UNDERLYING
GEOMETRY
-----
119
5.1.1
LINEAR
TYPE
----
120
5.1.2
HYPERPLANE
ARRANGEMENTS
----
121
5.1.3
BEHAVIOR
ALONG
A
FAMILY
-----
129
5.2
FREE
DIVISORS
-----
140
5.2.1
GENERAL
NONSENSE
----
140
5.2.2
ALGEBRAIC
LOGARITHMIC
VECTOR
FIELDS
-----
141
5.2.3
FAMILIES
OF
FREE
DIVISORS
-----
145
5.2.4
WEIGHTED
HOMOGENEOUS
DIVISORS
----
148
5.3
EXERCISES
-----
155
6
CREMONA
TRANSFORMATIONS,
I
-
159
6.1
PLANE
CREMONA
TRANSFORMATIONS:
HOMALOIDAL
NETS
----
159
6.1.1
WEIGHTED
CLUSTER
OF
BASE
POINTS
----
159
6.1.2
RELATION
TO
FAT
IDEALS
----
163
6.1.3
FROM
FAT
IDEALS
BACK
TO
THE
CREMONA
BASE
IDEAL
-
172
6.1.4
PROPER
HOMALOIDAL
TYPES
WITH
LARGE
HIGHEST
VIRTUAL
MULTIPLICITY
----
173
6.2
PLANE
CREMONA
TRANSFORMATIONS:
SUBHOMALOIDAL
TYPES
-
179
6.2.1
ARITHMETIC
QUADRATIC
TRANSFORMATIONS
ACTING
ON
FAT
POINTS
----
179
6.2.2
SUBHOMALOIDAL
MULTIPLICITY
SETS
-----
181
6.2.3
3-UNIFORM
SUBHOMALOIDAL
TYPES
-----
183
6.2.4
MAIN
THEOREM
----
199
CONTENTS
-
XIII
6.2.5
6.3
7
7.1
7.1.1
7.1.2
7.1.3
7.1.4
7.1.5
7.2
7.2.1
7.2.2
7.2.3
7.3
7.3.1
7.3.2
7.3.3
7.4
8
8.1
8.2
8.3
8.3.1
8.3.2
8.3.3
8.4
8.4.1
8.4.2
8.5
8.6
8.7
9
9.1
9.1.1
9.1.2
9.1.3
9.2
RELATION
TO
BORDIGA-WHITE
PARAMETRIZATIONS
----
203
EXERCISES
----
206
CREMONA
TRANSFORMATIONS,
II
-
209
GENERALIZED
DE
JONQUIERES
TRANSFORMATIONS
----
209
FULLY
DOWNGRADED
SEQUENCES
-
211
GENERALIZED
DE
JONQUIERES
TRANSFORMATIONS
----
213
GENERALIZED
DE
JONQUIERES
TRANSFORMATIONS
UNDER
NEWTON
DUALITY
----
215
GENERALIZED
DE
JONQUIERES
TRANSFORMATIONS
WITH
IDENTITY
SUPPORT
----
218
THE
MINIMAL
FREE
RESOLUTION
OF
THE
BASE
IDEAL
----
218
THE
GRAPH
(BLOWUP)
OF
A
CREMONA
MAP
----
220
THE
GRAPH
OF
A
DE
JONQUIERES
MAP
WITH
IDENTITY
SUPPORT
----
220
CREMONA
MAPS
WITH
A
COHEN-MACAULAY
GRAPH
----
227
CREMONA
MAPS
AND
SYMBOLIC
REES
ALGEBRAS
-
231
MONOMIAL
CREMONA
TRANSFORMATIONS
----
235
THE
GROUP
OF
MONOMIAL
CREMONA
TRANSFORMATIONS
----
235
MONOMIAL
CREMONA
TRANSFORMATIONS
OF
DEGREE
2
----
243
A
DUALITY
PRINCIPLE
----
256
EXERCISES
----
259
STEPS
IN
ELIMINATION
-
263
ELIMINATION
ALGEBRAS
----
263
IMPLICITIZATION
----
266
DE
JONQUIERES
LIKE
IMPLICITIZATION
----
267
ALGEBRAIC
PRELIMS
----
267
THE
(/F,G)-PARAMETRIZATION
----
268
THE
EQUATIONS
OF
THE
REES
ALGEBRA
----
273
IMPLICITIZATION
IN
DIMENSION
1
----
278
DIMENSION
ZERO
----
278
DIMENSION
ONE
----
293
THE
CLASSICAL
RESULTANT
----
295
ELIMINATING
FROM
CORRESPONDENCES
----
297
EXERCISES
----
300
THE
GAUSS
MAP
-
303
GAUSS
IMAGE
OF
HIGHER
ORDER
----
303
NOTABLE
CASES.
I:
THE
ORDINARY
GAUSS
IMAGE
----
305
NOTABLE
CASES.
II:
THE
DUAL
VARIETY
----
306
RELATION
TO
THE
TANGENTIAL
VARIETY
----
308
THE
GAUSS
IMAGE
OF
A
UNIRATIONAL
VARIETY
----
310
XIV
CONTENTS
9.2.1
THE
ALGEBRAIC
STRUCTURAL
DATA
-
310
9.2.2
THE
GAUSS
IMAGE
OF
TORIC
VARIETIES
----
313
9.2.3
ALGEBRAS
OF
VERONESE
TYPE
-
314
9.3
ABSTRACT
GAUSS
MAPS
----
316
9.4
THE
GEOMETRY
OF
THE
ANALYTIC
SPREAD
----
317
9.4.1
MAXIMAL
ANALYTIC
SPREAD
-
317
9.4.2
ANALYTIC
SPREAD
VERSUS
THE
FITTING
IDEAL
----
322
9.4.3
CASE
STUDY:
THE
MODULE
OF
DIFFERENTIALS
-
323
9.4.4
MAIN
THEOREM
OF
ABSTRACT
GAUSS
MAPS
----
325
9.5
EXERCISES
-----
329
10
TANGENT
VARIETIES
----
333
10.1
ALGEBRAIC
FULTON-HANSEN
THEOREMS
-----
333
10.1.1
ALGEBRAIC
PRELIMINARIES
-
333
10.1.2
THE
UNDERLYING
GEOMETRY
----
337
10.1.3
THE
TANGENTIAL
VARIETY
TO
A
UNIRATIONAL
VARIETY
-
340
10.2
REFINED
PROPERTIES
OF
TANGENT
ALGEBRAS
-
341
10.2.1
EXPECTED
STAR
DIMENSION
----
343
10.2.2
SET
THEORETIC
STARLIKE
LINEARITY
-----
347
10.2.3
STARLIKE
LINEARITY
-
348
10.2.4
BEHAVIOR
UNDER
FLAT
DEFORMATION
-
351
10.2.5
A
GLIMPSE
OF
THE
BLOWUP
OF
THE
KAHLER
DIFFERENTIALS
----
354
10.3
EXERCISES
-----
356
11
EMBEDDED
JOINSAND
SECANTS
-
359
11.1
JOINS
----
359
11.1.1
ALGEBRAIC
SIDE
-----
359
11.1.2
THE
GEOMETRIC
BACKGROUND
-----
360
11.1.3
RELATION
TO
THE
BAYER-MUMFORD
DEFORMATION
-
363
11.1.4
THE
EMBEDDED
JOIN
OF
A
UNION
OF
LINEAR
SPACES
-
366
11.1.5
INITIAL
DEGREE
OF
A
JOIN
-
368
11.2
SECANTS
-----
369
11.2.1
SECANTS
OF
DETERMINANTALAND
PFAFFIAN
SCHEMES
-
370
11.2.2
SECANTS
OFVARIETIES
CUT
BY
QUADRICS
-
374
11.2.3
SECANT
ALGEBRAS
OF
MONOMIAL
IDEALS
-
377
11.2.4
RELATION
TO
STARLIKE
LINEARITY
-
378
11.2.5
HIGHER
SECANTS
----
380
11.3
EXCERPTS
ON
THE
DIAGONAL
IDEAL
-
381
11.3.1
SYZYGIES
AND
DIMENSION
-----
382
11.3.2
THE
LINEAR
TYPE
PROPERTY
-----
383
11.4
EXERCISES
----
386
CONTENTS
XV
12
ALUFFI
ALGEBRAS
-
389
12.1
RELATION
TO
CHERN
CLASSES
-----
389
12.2
THE
CASE
OF
IDEALS:
EMBEDDED
VERSION
----
390
12.2.1
PRELIMINARIES
----
390
12.2.2
DIMENSION
----
392
12.2.3
TORSION
AND
MINIMAL
PRIMES
-----
395
12.2.4
RELATION
TO
THE
ARTIN-REES
NUMBER
----
398
12.2.5
SELECTED
EXAMPLES
----
402
12.2.6
THE
ALUFFI
ALGEBRA
OF
A
GRADIENT
IDEAL
----
405
12.3
THE
CASE
OF
MODULES
-----
407
12.3.1
THE
EMBEDDED
VERSION
-----
408
12.3.2
TAKING
INVERSE
LIMIT
-----
409
12.3.3
THE
MODULE
OF
DERIVATIONS
OF
A
POLYNOMIAL
FORM
----
413
12.3.4
THE
NORMAL
MODULE
OF
A
PERFECT
IDEAL
OF
CODIMENSION
2
----
421
12.4
EXERCISES
----
427
BIBLIOGRAPHY----
431
INDEX
----
441 |
| any_adam_object | 1 |
| any_adam_object_boolean | 1 |
| author | Simis, Aron 1942- Ramos, Zaqueu |
| author_GND | (DE-588)120670683X (DE-588)1264231784 |
| author_facet | Simis, Aron 1942- Ramos, Zaqueu |
| author_role | aut aut |
| author_sort | Simis, Aron 1942- |
| author_variant | a s as z r zr |
| building | Verbundindex |
| bvnumber | BV048488997 |
| classification_rvk | SK 240 |
| ctrlnum | (OCoLC)1310785505 (DE-599)DNB1245021982 |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV048488997 |
| illustrated | Not Illustrated |
| index_date | 2024-07-03T20:41:08Z |
| indexdate | 2024-11-25T15:01:40Z |
| institution | BVB |
| institution_GND | (DE-588)10095502-2 |
| isbn | 9783110637540 3110637545 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-033866510 |
| oclc_num | 1310785505 |
| open_access_boolean | |
| owner | DE-634 DE-20 |
| owner_facet | DE-634 DE-20 |
| physical | XV, 445 Seiten 24 cm, 876 g |
| publishDate | 2022 |
| publishDateSearch | 2022 |
| publishDateSort | 2022 |
| publisher | De Gruyter |
| record_format | marc |
| series | De Gruyter expositions in mathematics |
| series2 | De Gruyter expositions in mathematics |
| spelling | Simis, Aron 1942- Verfasser (DE-588)120670683X aut Graded algebras in algebraic geometry Aron Simis, Zaqueu Ramos Berlin De Gruyter [2022] XV, 445 Seiten 24 cm, 876 g txt rdacontent n rdamedia nc rdacarrier De Gruyter expositions in mathematics volume 70 Graduierter Ring (DE-588)4158003-5 gnd rswk-swf Kommutative Algebra (DE-588)4164821-3 gnd rswk-swf Algebraische Geometrie (DE-588)4001161-6 gnd rswk-swf Graduierter Modul Graduierter Ring Kommutative Algebra Schnitt <Mathematik> Algebraische Geometrie Algebraische Geometrie (DE-588)4001161-6 s Kommutative Algebra (DE-588)4164821-3 s Graduierter Ring (DE-588)4158003-5 s DE-604 Ramos, Zaqueu Verfasser (DE-588)1264231784 aut Walter de Gruyter GmbH & Co. KG (DE-588)10095502-2 pbl Erscheint auch als Online-Ausgabe Simis, Aron, 1942- Graded Algebras in Algebraic Geometry 1. Auflage Berlin/Boston : De Gruyter, 2022 Online-Ressource, 464 Seiten Erscheint auch als Online-Ausgabe 9783110640694 De Gruyter expositions in mathematics volume 70 (DE-604)BV004069300 70 X:MVB https://www.degruyter.com/isbn/9783110637540 B:DE-101 application/pdf https://d-nb.info/1245021982/04 Inhaltsverzeichnis DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=033866510&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p dnb 20220818 DE-101 https://d-nb.info/provenance/plan#dnb |
| spellingShingle | Simis, Aron 1942- Ramos, Zaqueu Graded algebras in algebraic geometry De Gruyter expositions in mathematics Graduierter Ring (DE-588)4158003-5 gnd Kommutative Algebra (DE-588)4164821-3 gnd Algebraische Geometrie (DE-588)4001161-6 gnd |
| subject_GND | (DE-588)4158003-5 (DE-588)4164821-3 (DE-588)4001161-6 |
| title | Graded algebras in algebraic geometry |
| title_auth | Graded algebras in algebraic geometry |
| title_exact_search | Graded algebras in algebraic geometry |
| title_exact_search_txtP | Graded algebras in algebraic geometry |
| title_full | Graded algebras in algebraic geometry Aron Simis, Zaqueu Ramos |
| title_fullStr | Graded algebras in algebraic geometry Aron Simis, Zaqueu Ramos |
| title_full_unstemmed | Graded algebras in algebraic geometry Aron Simis, Zaqueu Ramos |
| title_short | Graded algebras in algebraic geometry |
| title_sort | graded algebras in algebraic geometry |
| topic | Graduierter Ring (DE-588)4158003-5 gnd Kommutative Algebra (DE-588)4164821-3 gnd Algebraische Geometrie (DE-588)4001161-6 gnd |
| topic_facet | Graduierter Ring Kommutative Algebra Algebraische Geometrie |
| url | https://www.degruyter.com/isbn/9783110637540 https://d-nb.info/1245021982/04 http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=033866510&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV004069300 |
| work_keys_str_mv | AT simisaron gradedalgebrasinalgebraicgeometry AT ramoszaqueu gradedalgebrasinalgebraicgeometry AT walterdegruytergmbhcokg gradedalgebrasinalgebraicgeometry |
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