Relative moduli spaces of semi-stable sheaves on families of curves:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
München
Utz, Wiss.
2001
|
| Schriftenreihe: | Mathematik
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Zugl.: München, Univ., Diss., 2000 |
| Beschreibung: | X, 143 21 cm |
| ISBN: | 3896758942 |
Internformat
MARC
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| 100 | 1 | |a Lang, Jens Thomas Alexander |d 1970- |e Verfasser |0 (DE-588)122692659 |4 aut | |
| 245 | 1 | 0 | |a Relative moduli spaces of semi-stable sheaves on families of curves |c Jens Thomas Alexander Lang |
| 264 | 1 | |a München |b Utz, Wiss. |c 2001 | |
| 300 | |a X, 143 |b 21 cm | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Mathematik | |
| 500 | |a Zugl.: München, Univ., Diss., 2000 | ||
| 650 | 0 | 7 | |a Familie |g Mathematik |0 (DE-588)4204324-4 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Modulraum |0 (DE-588)4183462-8 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Garbe |g Mathematik |0 (DE-588)4019261-1 |2 gnd |9 rswk-swf |
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| 689 | 0 | 1 | |a Garbe |g Mathematik |0 (DE-588)4019261-1 |D s |
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Datensatz im Suchindex
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| adam_text |
CONTENTS
1
INTRODUCTION
11
1.1
INTRODUCTION
AND
MOTIVATION
.
11
1.1.1
RELATIVE
MODULI
SPACES
.
11
1.1.2
RELATIVE
MODULI
SPACES
OF
SHEAVES
ON
CURVES
.
12
1.1.3
PHYSICAL
MOTIVATION
.
YY
.
13
1.1.4
DEGENERATION
ARGUMENTS
.
14
1.1.5
MOTIVATION
-
SUMMARY
.
15
1.2
CONVENTIONS
.
16
1.3
CONTENTS
AND
DESCRIPTION
OF
MY
OWN
RESULTS
.
17
1.3.1
NOTE
.
19
1.4
ACKNOWLEDGEMENTS
.
19
2
ABSOLUTE
AND
RELATIVE
MODULI
SPACES
IN
GENERAL
20
2.1
MOTIVATION
.
20
2.2
FAMILY
OF
OBJECTS
.
21
2.3
FINE
MODULI
SPACES
.
22
2.4
COARSE
MODULI
SPACES
.
24
2.5
RELATIVE
MODULI
FUNCTORS
.
26
2.5.1
RELATIVE
FAMILIES
.
27
2.5.2
RELATIVE
MODULI
FUNCTOR
.
27
2.6
RELATIVE
MODULI
SPACES
.
27
2.6.1
FINE
RELATIVE
MODULI
SPACES
.
27
2.6.2
COARSE
RELATIVE
MODULI
SPACES
.
28
2.6.3
BEHAVIOUR
OF
RELATIVE
MODULI
PROBLEMS
UNDER
PULLBACK
.
29
2.7
THE
RELATIVE
MODULI
SPACES
VERSUS
ABSOLUTE
MODULI
SPACES
.
31
2.7.1
THE
RELATIVE
CASE
IS
A
TRUE
GENERALIZATION
.
31
2.7.2
THE
RELATIVE
MODULI
SPACE
IS
A
FAMILY
OF
ABSOLUTE
MODULI
SPACES
31
3
ABSOLUTE
MODULI
SPACES
OF
SEMI-STABLE
SHEAVES
ON
A
CURVE
33
3.1
OUR
CURVES
.
33
3.2
SEMI-STABILITY:
DEFINITIONS
AND
CLASSICAL
RESULTS
.
34
3.2.1
NOTIONS
ASSOCIATED
TO
SHEAVES
.
34
3.2.2
(SEMI-)STABILITY
FOR
GENERAL
PROJECTIVE
POLARIZED
K-VARIETIES
X
.
.
36
3.2.3
(SEMI-)STABILITY
FOR
PROJECTIVE
CURVES
X
.
36
3.3
FAMILIES
OF
SHEAVES
AND
VECTOR
BUNDLES
.
37
3.3.1
DEFINITIONS
.
37
3.4
MODULI
FUNCTORS
.
38
3.5
THE
MODULI
SPACES
AND
THEIR
PROPERTIES
.
39
4
ABSOLUTE
MODULI
SPACES
OF
SEMI-STABLE
SHEAVES
ON
A
NODAL
CURVE
41
4.1
KNOWN
RESULTS
.
'
.
42
4.2
VECTOR
BUNDLES
ON
A
NODAL
CURVE
AND
ON
ITS
NORMALIZATION
.
42
4.2.1
ALGEBRAIC
TREATMENT
.
43
4.2.2
EXPLICIT
TREATMENT
IN
THE
STRONG
TOPOLOGY
.
46
4.3
MAPS
BETWEEN
MX
(R,D)
AND
M^(R,D)
.
48
4.4
THE
MODULI
SPACE
MY
.
52
4.5
THE
MODULI
SPACE
M
(R,
D)
OVER
A
CURVE
WITH
AN
ORDINARY
DOUBLE
POINT
54
5
THE
RELATIVE
MODULI
PROBLEM
OF
SEMI-STABLE
SHEAVES
ON
CURVES
56
5.1
FAMILIES
OF
RIEMANNIAN
SURFACES
.
56
5.1.1
DEFINITION
.
56
5.1.2
EXISTENCE
OF
SUCH
FAMILIES
.
57
5.1.3
AMPLE
LINE
BUNDLES
.
58
5.2
DISCUSSION
OF
RELATIVE
NOTIONS
.
58
5.2.1
FIRST
ATTEMPT
.
59
5.2.2
SECOND
ATTEMPT
.
59
5.2.3
BEST
ATTEMPT
.
60
5.3
RELATIVE
FAMILIES
.
60
5.3.1
DEFINITIONS
.
60
5.3.2
RELATIONSHIP
OF
HILBERT
POLYNOMIAL
VERSUS
RANK
AND
DEGREE
IN
THE
RELATIVE
CASE
.
61
5.3.3
EXAMPLES
.
61
5.4
THE
RELATIVE
MODULI
FUNCTOR
.
62
5.5
A
FIRST
APPROACH
TO
FINDING
M
.
63
6
EXISTENCE
OF
RELATIVE
MODULI
SPACES
OF
SHEAVES
ON
CURVES
65
6.1
NECESSITY
OF
SEMI-STABILITY
.
65
6.2
BOUNDED
FAMILIES
.
66
6.2.1
DEFINITION
.
66
6.2.2
CONTROLLING
H
1
.
67
6.2.3
A
BOUNDEDNESS-RESULT
.
68
6.3
THE
RELATIVE
QUOT-SCHEME
QUOT
.
68
6.3.1
THE
MODULI
FUNCTOR
OF
RELATIVE
QUOTIENTS
OF
A
SHEAF
.
68
6.3.2
THE
FINE
MODULI
SPACE
OF
RELATIVE
QUOTIENTS
OF
A
SHEAF
.
69
6.4
THE
GIT-CONSTRUCTION
.
69
6.4.1
SEMI-STABILITY
.
69
6.4.2
THE
SPACE
77
"
.
69
6.4.3
TAKING
THE
GIT-QUOTIENT
OF
77
"
.
70
6.4.4
77
"
//G
IS
THE
UNIVERSAL
COARSE
MODULI
SPACE
.
70
6.5
WHEN
IS
A4(R,D)
A
FINE
MODULI
SPACE?
.
70
6.6
THE
RELATIVE
MODULI
SPACE
IMPLIES
THE
ABSOLUTE
ONE
.
71
VIII
7
FROM
THE
FIBRES
TO
THE
WHOLE
SPACE
-
GENERAL
RESULTS
76
7.1
A
COUNTEREXAMPLE
.
75
7.2
RESULTS
.
76
7.2.1
IRREDUCIBILITY
.
76
7.2.2
FLATNESS
.
78
8
PROPERTIES
OF
RELATIVE
MODULI
SPACES
OF
SHEAVES
ON
CURVES
80
8.1
THE
RELATIVE
MODULI
SPACE
M(R.D)
IS
A
VARIETY
.
80
8.1.1
ALTERNATIVE
PROOFS
.
81
8.2
A4(R,D)
IS
NORMAL
FOR
SMOOTH
CURVES
.
82
8.3
M(R,D)
IS
LOCALLY
FACTORIAL
.
84
8.3.1
PROLONGATION
OF
LINE
BUNDLES
ON
M(R,D)
.
84
8.4
ON
THE
EXISTENCE
OF
SECTIONS
OF
?R
:
X
-4
B
AND
M{R,
D)
-
B
.
89
8.4.1
EXISTENCE
OF
SECTIONS
OF
%
:
X
-+
B
.
89
8.4.2
EXISTENCE
OF
FAMILIES
OF
SEMI-STABLE
SHEAVES
.
89
8.4.3
EXISTENCE
OF
SECTIONS
OF
M
-+
B
.
90
8.5
AN
EXAMPLE
.
90
9
RELATIVE
MODULI
SPACES
OF
SHEAVES
WITH
FIXED
DETERMINANT
ON
SMOOTH
CURVES
92
9.1
THE
DETERMINANT
ON
FAMILIES
OF
SHEAVES
.
92
9.2
THE
DETERMINANT
MAP
.
94
9.3
DEFINITION
AND
EXISTENCE
OF
M(R,
.)
.
95
9.4
PROPERTIES
OF
M
(R,)
.
96
10
MODULI
SPACES
OF
SHEAVES
WITH
FIXED
DETERMINANT
ON
NODAL
CURVES
99
10.1
THE
ABSOLUTE
CASE
.
99
10.2
THE
RELATIVE
CASE
.
100
10.3
OTHER
MODULI
SPACES
.
101
10.4
A
CONJECTURE
OF
SESHADRI
.
102
11
THE
THETA-BUNDLE
ON
THE
RELATIVE
MODULI
SPACE
103
11.0.1
THE
CLASSICAL
THETA
BUNDLE
.
103
11.1
THE
THETA
BUNDLES
ON
THE
ABSOLUTE
MODULI
SPACES
.
104
11.1.1
THE
THETA
BUNDLE
AS
GENERATOR
OF
THE
PICARD
GROUP
.
104
11.1.2
THE
THETA
DIVISOR
.
105
11.1.3
THETA
BUNDLES
AS
UNIVERSAL
DETERMINANT
BUNDLES
.
105
11.1.4
APPROACH
OF
DONAGI-TU
.
106
11.1.5
NODAL
CURVES:
CONSTRUCTION
BY
NARASIMHAN-RAMADAS,
SUN
.
.
.
107
11.2
RELATIVE
THETA
BUNDLES
OR
FAMILIES
OF
THETA
BUNDLES
.
108
11.2.1
THE
RELATIVE
THETA
DIVISOR
.
109
11.2.2
GENERALIZATION
OF
THE
DONAGI-TU
APPROACH
.
110
11.2.3
THE
UNIVERSAL
DETERMINANT
BUNDLE
.
ILL
11.2.4
GENERALIZATION
OF
THE
NARASIMHAN-RAMADAS-SUN
APPROACH
.
.
.
112
IX
12
THE
VECTOR-BUNDLE
OF
CONFORMAL
BLOCKS
116
12.1
CONFORMAL
BLOCKS
AND
VERLINDE
FORMULA
.
116
12.1.1
CONFORMAL
BLOCKS
AND
SECTIONS
OF
THE
THETA
BUNDLE
.
116
12.2
THE
VECTOR
BUNDLE
E
(,)
OF
CONFORMAL
BLOCKS
.
117
12.2.1
E^
CONSTRUCTED
WITH
RESPECT
TO
M(R,D)
.
117
12.2.2
E^
CONSTRUCTED
WITH
RESPECT
TO
M(R,
C)
.
118
12.3
THE
PROJECTIVELY
FLAT
CONNECTION
ON
E
(L
=
JT
,
OVER
B
.
.
.
119
12.4
EXTENDING
THE
HITCHIN-CONNECTION
.
120
A
COLLECTION
OF
KNOWN
FACTS
AND
TOOLS
IN
ALGEBRAIC
GEOMETRY
121
A.L
TOOLS
FROM
ALGEBRAIC
GEOMETRY
.
121
A.2
TOOLS
FROM
ANALYTIC
GEOMETRY
.
124
B
AN
EXPLICIT
EXAMPLE
OF
A
FAMILY
OF
CURVES
125
B.L
FLAT
MAPS
.
128
C
BACKGROUND
AND
MOTIVATION
FROM
PHYSICS
130
C.L
TOPOLOGICAL
QUANTUM
FIELD
THEORIES
.
130
C.2
CONFORMAL
FIELD
THEORIES
.
131
C.3
GEOMETRIC
QUANTIZATION
.
131
C.4
THE
VERLINDE
FORMULA
.
133
C.4.1
THE
HITCHIN
CONNECTION
.
133
X |
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| genre | (DE-588)4113937-9 Hochschulschrift gnd-content |
| genre_facet | Hochschulschrift |
| id | DE-604.BV013616925 |
| illustrated | Not Illustrated |
| indexdate | 2024-08-16T01:08:26Z |
| institution | BVB |
| isbn | 3896758942 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-009303621 |
| oclc_num | 50486374 |
| open_access_boolean | |
| owner | DE-12 DE-19 DE-BY-UBM |
| owner_facet | DE-12 DE-19 DE-BY-UBM |
| physical | X, 143 21 cm |
| publishDate | 2001 |
| publishDateSearch | 2001 |
| publishDateSort | 2001 |
| publisher | Utz, Wiss. |
| record_format | marc |
| series2 | Mathematik |
| spelling | Lang, Jens Thomas Alexander 1970- Verfasser (DE-588)122692659 aut Relative moduli spaces of semi-stable sheaves on families of curves Jens Thomas Alexander Lang München Utz, Wiss. 2001 X, 143 21 cm txt rdacontent n rdamedia nc rdacarrier Mathematik Zugl.: München, Univ., Diss., 2000 Familie Mathematik (DE-588)4204324-4 gnd rswk-swf Modulraum (DE-588)4183462-8 gnd rswk-swf Garbe Mathematik (DE-588)4019261-1 gnd rswk-swf (DE-588)4113937-9 Hochschulschrift gnd-content Modulraum (DE-588)4183462-8 s Garbe Mathematik (DE-588)4019261-1 s Familie Mathematik (DE-588)4204324-4 s DE-604 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009303621&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Lang, Jens Thomas Alexander 1970- Relative moduli spaces of semi-stable sheaves on families of curves Familie Mathematik (DE-588)4204324-4 gnd Modulraum (DE-588)4183462-8 gnd Garbe Mathematik (DE-588)4019261-1 gnd |
| subject_GND | (DE-588)4204324-4 (DE-588)4183462-8 (DE-588)4019261-1 (DE-588)4113937-9 |
| title | Relative moduli spaces of semi-stable sheaves on families of curves |
| title_auth | Relative moduli spaces of semi-stable sheaves on families of curves |
| title_exact_search | Relative moduli spaces of semi-stable sheaves on families of curves |
| title_full | Relative moduli spaces of semi-stable sheaves on families of curves Jens Thomas Alexander Lang |
| title_fullStr | Relative moduli spaces of semi-stable sheaves on families of curves Jens Thomas Alexander Lang |
| title_full_unstemmed | Relative moduli spaces of semi-stable sheaves on families of curves Jens Thomas Alexander Lang |
| title_short | Relative moduli spaces of semi-stable sheaves on families of curves |
| title_sort | relative moduli spaces of semi stable sheaves on families of curves |
| topic | Familie Mathematik (DE-588)4204324-4 gnd Modulraum (DE-588)4183462-8 gnd Garbe Mathematik (DE-588)4019261-1 gnd |
| topic_facet | Familie Mathematik Modulraum Garbe Mathematik Hochschulschrift |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009303621&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT langjensthomasalexander relativemodulispacesofsemistablesheavesonfamiliesofcurves |