Projective duality and homogeneous spaces:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin [u.a.]
Springer
2005
|
| Series: | Encyclopaedia of mathematical sciences
133 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIV, 250 S. graph. Darst. |
| ISBN: | 3540228985 |
Staff View
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| 100 | 1 | |a Tevelev, Evgueni A. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Projective duality and homogeneous spaces |c E. A. Tevelev |
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 2005 | |
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Record in the Search Index
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|---|---|
| adam_text | CONTENTS
1
INTRODUCTION
TO
PROJECTIVE
DUALITY
.........................
1
1.1
PROJECTIVELY
DUAL
VARIETIES
...............................
1
1.2
DUAL
PLANE
CURVES.......................................
2
1.2.1
PARAMETRIC
EQUATIONS..............................
2
1.2.2
LEGENDRE
TRANSFORMATION...........................
3
1.2.3
PL
UCKER
FORMULAS..................................
4
1.2.4
CURVES
OF
SMALL
DEGREE
............................
5
1.3
RE EXIVITY
THEOREM
.....................................
6
1.3.1
PROOF
OF
THE
RELEXIVITY
THEOREM
....................
6
1.3.2
DEFECT
AND
DISCRIMINANT
...........................
9
1.4
PROJECTIONS
AND
LINEAR
NORMALITY
.........................
11
1.4.1
PROJECTIONS
.......................................
11
1.4.2
DEGENERATE
VARIETIES
...............................
12
1.4.3
LINEAR
NORMALITY..................................
13
2
ACTIONS
WITH
FINITELY
MANY
ORBITS
........................
17
2.1
ALGEBRAIC
GROUPS........................................
17
2.2
PYASETSKII
PAIRING
AND
KASHIN
EXAMPLES
...................
32
2.3
ACTIONS
RELATED
TO
GRADINGS
..............................
35
2.3.1
CONSTRUCTION......................................
35
2.3.2
SHORT
GRADINGS....................................
41
2.3.3
MULTISEGMENT
DUALITY..............................
49
3
LOCAL
CALCULATIONS
.........................................
57
3.1
CALCULATIONS
IN
COORDINATES...............................
57
3.1.1
KATZ
DIMENSION
FORMULA
...........................
57
3.1.2
DEFECT
OF
A
PRODUCT................................
60
3.2
FUNDAMENTAL
FORMS......................................
64
3.2.1
SECOND
FUNDAMENTAL
FORM
.........................
64
3.2.2
HIGHER
FUNDAMENTAL
FORMS
.........................
67
3.2.3
FUNDAMENTAL
FORMS
OF
FLAG
VARIETIES
................
70
XII
CONTENTS
4
PROJECTIVE
CONSTRUCTIONS
..................................
73
4.1
GAUSS
MAP
.............................................
73
4.2
TANGENTS
AND
SECANTS
....................................
74
4.2.1
TERRACINI
LEMMA
..................................
74
4.2.2
MULTISECANT
VARIETIES
OF
HOMOGENEOUS
SPACES
.........
75
4.2.3
DEG
X
FFL
AND
ORD
X
.................................
77
4.2.4
WARING
PROBLEM
FOR
FORMS
.........................
79
4.3
ZAK
THEOREMS
..........................................
80
4.3.1
THEOREM
ON
TANGENCIES
............................
80
4.3.2
THEOREM
ON
LINEAR
NORMALITY.......................
82
4.3.3
THEOREM
ON
SEVERI
VARIETIES
........................
83
4.3.4
CONNECTEDNESS
THEOREM
OF
FULTON
AND
HANSEN
........
84
4.4
CHOW
FORMS
............................................
87
5
VECTOR
BUNDLES
METHODS
..................................
89
5.1
DUAL
VARIETIES
OF
SMOOTH
DIVISORS
.........................
89
5.1.1
LINEAR
ENVELOPE
OF
A
TANGENTIAL
VARIETY
..............
89
5.1.2
DUAL
VARIETIES
OF
SMOOTH
DIVISORS
...................
91
5.1.3
PROJECTIVE
EXTENDABILITY............................
93
5.2
AMPLE
VECTOR
BUNDLES
...................................
94
5.2.1
DEYYNITIONS
.......................................
94
5.2.2
DUAL
VARIETIES
OF
SMOOTH
COMPLETE
INTERSECTIONS
......
95
5.2.3
RESULTANTS........................................
96
5.3
CAYLEY
METHOD..........................................
97
5.3.1
JET
BUNDLES
AND
KOSZUL
COMPLEXES
..................
97
5.3.2
CAYLEY
DETERMINANTS
OF
EXACT
COMPLEXES
............
99
5.3.3
DISCRIMINANT
COMPLEXES............................102
5.3.4
CAYLEY
METHOD
FOR
RESULTANTS.......................105
6
DEGREE
OF
THE
DUAL
VARIETY
................................109
6.1
KATZ{KLEIMAN{HOLME
FORMULA
............................109
6.1.1
CHERN
CLASSES.....................................109
6.1.2
TOP
CHERN
CLASS
OF
THE
JET
BUNDLE
..................110
6.1.3
FORMULAS
WITH
POSITIVE
COEYYCIENTS
..................113
6.1.4
DEGREE
OF
THE
RESULTANT
............................114
6.2
FORMULAS
RELATED
TO
THE
CAYLEY
METHOD....................115
6.2.1
DEGREE
OF
THE
DISCRMINANT..........................115
6.2.2
LASCOUX
FORMULA
..................................116
7
VARIETIES
WITH
POSITIVE
DEFECT
.............................119
7.1
NORMAL
BUNDLE
OF
THE
CONTACT
LOCUS.......................119
7.1.1
EIN
THEOREMS.....................................119
7.1.2
MONOTONICITY
THEOREM.............................124
7.1.3
BEILINSON
SPECTRAL
SEQUENCE
........................124
7.1.4
PLANES
IN
THE
CONTACT
LOCUS
........................126
CONTENTS
XIII
7.1.5
SCROLLS
...........................................129
7.2
LINEAR
SYSTEMS
OF
QUADRICS
OF
CONSTANT
RANK...............130
7.3
DEFECT
AND
NEF
VALUE
....................................136
7.3.1
SOME
RESULTS
FROM
MORI
THEORY.....................136
7.3.2
THE
NEF
VALUE
AND
THE
DEFECT.......................140
7.3.3
VARIETIES
WITH
SMALL
DUAL
VARIETIES
..................145
7.4
FLAG
VARIETIES
WITH
POSITIVE
DEFECT.........................147
7.4.1
NEF
CONE
OF
A
FLAG
VARIETY
.........................147
7.4.2
NEF
VALUES
OF
FLAG
VARIETIES.........................149
7.4.3
FLAG
VARIETIES
OF
POSITIVE
DEFECT.....................150
8
DUAL
VARIETIES
OF
HOMOGENEOUS
SPACES
....................155
8.1
CALCULATIONS
OF
DEG
X
FFL
...................................155
8.1.1
BOREL{WEYL{BOTT
THEOREM
.........................155
8.1.2
REPRESENTATION
THEORY
OF
GL
N
......................157
8.1.3
DUAL
VARIETY
OF
THE
GRASSMANNIAN...................158
8.1.4
CODEGREE
OF
G=B
..................................159
8.1.5
A
CLOSED
FORMULA
.................................161
8.1.6
DEGREE
OF
HYPERDETERMINANTS
.......................166
8.1.7
VARIETIES
OF
SMALL
CODEGREE.........................167
8.2
MATSUMURA{MONSKY
THEOREM.............................169
8.3
DISCRIMINANTS
OF
COMMUTATIVE
ALGEBRAS
....................171
8.3.1
COMMUTATIVE
ALGEBRAS
WITHOUT
IDENTITIES
............171
8.3.2
QUASIDERIVATIONS
..................................172
8.4
DISCRIMINANTS
OF
ANTICOMMUTATIVE
ALGEBRAS.................174
8.4.1
GENERIC
ANTICOMMUTATIVE
ALGEBRAS
..................174
8.4.2
REGULAR
ALGEBRAS..................................179
8.4.3
REGULAR
4-DIMENSIONAL
ANTICOMMUTATIVE
ALGEBRAS
.....181
8.4.4
DODECAHEDRAL
SECTION
..............................183
8.5
ADJOINT
VARIETIES
........................................186
8.6
HOMOGENEOUS
VECTOR
BUNDLES
.............................189
8.6.1
ZEROS
OF
GENERIC
GLOBAL
SECTIONS
....................189
8.6.2
ISOTROPIC
SUBSPACES
OF
FORMS
.......................192
8.6.3
MOORE{PENROSE
INVERSE
AND
APPLICATIONS
.............196
9
SELF-DUAL
VARIETIES
.........................................207
9.1
SMOOTH
SELF-DUAL
VARIETIES................................207
9.1.1
SELF-DUAL
FLAG
VARIETIES.............................207
9.1.2
HARTSHORNE
CONJECTURE
.............................209
9.1.3
EIN S
THEOREM
....................................210
9.1.4
FINITENESS
THEOREM................................212
9.2
SELF-DUAL
NILPOTENT
ORBITS................................213
XIV
CONTENTS
10
SINGULARITIES
OF
DUAL
VARIETIES
.............................219
10.1
CLASS
FORMULA...........................................219
10.2
SINGULARITIES
OF
X
FFL
.......................................222
10.2.1
MILNOR
NUMBERS...................................222
10.2.2
MILNOR
CLASS......................................224
10.2.3
DUAL
VARIETY
OF
A
SURFACE...........................228
10.2.4
SINGULARITIES
OF
HYPERDETERMINANTS
..................231
REFERENCES
.....................................................233
INDEX
..........................................................245
|
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| author_sort | Tevelev, Evgueni A. |
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| ctrlnum | (OCoLC)440663797 (DE-599)BVBBV019590465 |
| discipline | Mathematik |
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| id | DE-604.BV019590465 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T20:00:58Z |
| institution | BVB |
| isbn | 3540228985 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-012927230 |
| oclc_num | 440663797 |
| open_access_boolean | |
| owner | DE-703 DE-19 DE-BY-UBM DE-91G DE-BY-TUM DE-355 DE-BY-UBR DE-11 DE-188 |
| owner_facet | DE-703 DE-19 DE-BY-UBM DE-91G DE-BY-TUM DE-355 DE-BY-UBR DE-11 DE-188 |
| physical | XIV, 250 S. graph. Darst. |
| publishDate | 2005 |
| publishDateSearch | 2005 |
| publishDateSort | 2005 |
| publisher | Springer |
| record_format | marc |
| series | Encyclopaedia of mathematical sciences |
| series2 | [Encyclopaedia of mathematical sciences / Invariant theory and algebraic transformation groups] Encyclopaedia of mathematical sciences |
| spelling | Tevelev, Evgueni A. Verfasser aut Projective duality and homogeneous spaces E. A. Tevelev Berlin [u.a.] Springer 2005 XIV, 250 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier [Encyclopaedia of mathematical sciences / Invariant theory and algebraic transformation groups] 4 Encyclopaedia of mathematical sciences 133 Dualität (DE-588)4013161-0 gnd rswk-swf Homogener Raum (DE-588)4025787-3 gnd rswk-swf Projektive Varietät (DE-588)4327070-0 gnd rswk-swf Projektive Varietät (DE-588)4327070-0 s Dualität (DE-588)4013161-0 s Homogener Raum (DE-588)4025787-3 s DE-604 Invariant theory and algebraic transformation groups] [Encyclopaedia of mathematical sciences 4 (DE-604)BV014336202 4 Encyclopaedia of mathematical sciences 133 (DE-604)BV024126459 133 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=012927230&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Tevelev, Evgueni A. Projective duality and homogeneous spaces Encyclopaedia of mathematical sciences Dualität (DE-588)4013161-0 gnd Homogener Raum (DE-588)4025787-3 gnd Projektive Varietät (DE-588)4327070-0 gnd |
| subject_GND | (DE-588)4013161-0 (DE-588)4025787-3 (DE-588)4327070-0 |
| title | Projective duality and homogeneous spaces |
| title_auth | Projective duality and homogeneous spaces |
| title_exact_search | Projective duality and homogeneous spaces |
| title_full | Projective duality and homogeneous spaces E. A. Tevelev |
| title_fullStr | Projective duality and homogeneous spaces E. A. Tevelev |
| title_full_unstemmed | Projective duality and homogeneous spaces E. A. Tevelev |
| title_short | Projective duality and homogeneous spaces |
| title_sort | projective duality and homogeneous spaces |
| topic | Dualität (DE-588)4013161-0 gnd Homogener Raum (DE-588)4025787-3 gnd Projektive Varietät (DE-588)4327070-0 gnd |
| topic_facet | Dualität Homogener Raum Projektive Varietät |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=012927230&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV014336202 (DE-604)BV024126459 |
| work_keys_str_mv | AT tevelevevguenia projectivedualityandhomogeneousspaces |