Real Lefschetz fibrations:
Saved in:
| Main Author: | |
|---|---|
| Format: | Thesis Book |
| Language: | English |
| Published: |
Strasbourg
IRMA, Univ. Louis Pasteur et C.N.R.S.
2007
|
| Series: | [Prépublication de l']Institut de Recherche Mathématique Avancée
2007,8 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Text engl., Einl. franz. |
| Physical Description: | 135 S. graph. Darst. |
Staff View
MARC
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| 245 | 1 | 0 | |a Real Lefschetz fibrations |c par Nermin Salepci |
| 264 | 1 | |a Strasbourg |b IRMA, Univ. Louis Pasteur et C.N.R.S. |c 2007 | |
| 300 | |a 135 S. |b graph. Darst. | ||
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| 490 | 1 | |a [Prépublication de l']Institut de Recherche Mathématique Avancée |v 2007,8 | |
| 500 | |a Text engl., Einl. franz. | ||
| 502 | |a Zugl.: Strasbourg, Univ., Diss., 2007 | ||
| 650 | 7 | |a Geometria algébrica real (tese doutorado) |2 larpcal | |
| 650 | 0 | 7 | |a Faserung |g Mathematik |0 (DE-588)4472884-0 |2 gnd |9 rswk-swf |
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Record in the Search Index
| _version_ | 1804138124826116096 |
|---|---|
| adam_text | Contents
1
Introduction
9
2
Preliminaries
17
2.1 Lefschetz fibrations............................. 17
2.2
Real Lefschetz fibrations
.......................... 20
3
Factorization of the monodromy of real Lefschetz fibrations
25
3.1
Fundamental factorization theorem for real Lefschetz fibrations
.... 25
3.2
Homology monodromy factorization of elliptic F-fibrations
....... 28
3.3
The modular action on the hyperbolic half-plane
............ 30
3.4
The Farey Tessellation
........................... 31
3.5
Elliptic and parabolic matrices
...................... 32
3.6
Hyperbolic matrices
............................ 33
3.7
Real factorization of elliptic and parabolic matrices
........... 36
3.8
Criterion of factorizability for hyperbolic matrices
........... 38
4
Real Lefschetz fibrations around singular fibers
43
4.1
Elementary Lefschetz fibrations
...................... 43
4.2
Elementary Real Lefschetz fibrations
................... 47
4.3
Vanishing cycles of real Lefschetz fibrations
............... 53
4.4
Classification of elementary real Lefschetz fibrations with nonseparating
vanishing cycles
............................... 55
4.5
Classification of elementary real Lefschetz fibrations with separating
vanishing cycles
............................... 60
Contents
5
Invariants
of real Lefschetz flbrations with only real critical values
65
5.1
Boundary fiber sum of genus-g real Lefschetz fibrations
........ 65
5.2
Equivariant diffeomorphisms and the space of real structures
..... 67
5.3
Real Lefschetz chains
............................ 75
5.4
Real elliptic Lefschetz fibrations with real sections and pointed real
Lefschetz chains
............................... 77
5.5
Real elliptic Lefschetz fibrations without real sections
......... 80
5.6
Weak real Lefschetz chains
......................... 88
6
Necklace Diagrams
95
6.1
Real locus of real elliptic Lefschetz fibrations with real sections
.... 95
6.2
Monodromy representation of stones
................... 99
6.3
The Correspondence Theorem
....................... 102
6.4
Refined necklace diagrams
......................... 103
6.5
The
Euler
characteristic and the
Betti
numbers of necklace diagrams
. 106
6.6
Horizontal and vertical transformations of necklace diagrams
..... 107
6.7
Producing new necklace diagrams using necklace connected sum
. . . 109
6.8
Classification of real E(l) with real sections via necklace diagrams
. . 110
6.9
Real elliptic Lefschetz fibrations of type
E
(2)
with real sections
.... 112
6.10
Some other applications of necklace diagrams
.............. 114
A Algebraicity of real elliptic Lefschetz fibrations with a section
117
A.I Trigonal curves on Hirzebruch surfaces
.................. 117
A.2 Real
dessins d enfants
associated to trigonal curves
........... 118
A.3 Correspondence between real schemes and real
dessins d enfants .
... 119
A.4 Algebraicity of real elliptic Lefschetz fibrations with real sections
. . . 121
Bibliography
123
Index of symbols
131
Index
134
|
| adam_txt |
Contents
1
Introduction
9
2
Preliminaries
17
2.1 Lefschetz fibrations. 17
2.2
Real Lefschetz fibrations
. 20
3
Factorization of the monodromy of real Lefschetz fibrations
25
3.1
Fundamental factorization theorem for real Lefschetz fibrations
. 25
3.2
Homology monodromy factorization of elliptic F-fibrations
. 28
3.3
The modular action on the hyperbolic half-plane
. 30
3.4
The Farey Tessellation
. 31
3.5
Elliptic and parabolic matrices
. 32
3.6
Hyperbolic matrices
. 33
3.7
Real factorization of elliptic and parabolic matrices
. 36
3.8
Criterion of factorizability for hyperbolic matrices
. 38
4
Real Lefschetz fibrations around singular fibers
43
4.1
Elementary Lefschetz fibrations
. 43
4.2
Elementary Real Lefschetz fibrations
. 47
4.3
Vanishing cycles of real Lefschetz fibrations
. 53
4.4
Classification of elementary real Lefschetz fibrations with nonseparating
vanishing cycles
. 55
4.5
Classification of elementary real Lefschetz fibrations with separating
vanishing cycles
. 60
Contents
5
Invariants
of real Lefschetz flbrations with only real critical values
65
5.1
Boundary fiber sum of genus-g real Lefschetz fibrations
. 65
5.2
Equivariant diffeomorphisms and the space of real structures
. 67
5.3
Real Lefschetz chains
. 75
5.4
Real elliptic Lefschetz fibrations with real sections and pointed real
Lefschetz chains
. 77
5.5
Real elliptic Lefschetz fibrations without real sections
. 80
5.6
Weak real Lefschetz chains
. 88
6
Necklace Diagrams
95
6.1
Real locus of real elliptic Lefschetz fibrations with real sections
. 95
6.2
Monodromy representation of stones
. 99
6.3
The Correspondence Theorem
. 102
6.4
Refined necklace diagrams
. 103
6.5
The
Euler
characteristic and the
Betti
numbers of necklace diagrams
. 106
6.6
Horizontal and vertical transformations of necklace diagrams
. 107
6.7
Producing new necklace diagrams using necklace connected sum
. . . 109
6.8
Classification of real E(l) with real sections via necklace diagrams
. . 110
6.9
Real elliptic Lefschetz fibrations of type
E
(2)
with real sections
. 112
6.10
Some other applications of necklace diagrams
. 114
A Algebraicity of real elliptic Lefschetz fibrations with a section
117
A.I Trigonal curves on Hirzebruch surfaces
. 117
A.2 Real
dessins d'enfants
associated to trigonal curves
. 118
A.3 Correspondence between real schemes and real
dessins d'enfants .
. 119
A.4 Algebraicity of real elliptic Lefschetz fibrations with real sections
. . . 121
Bibliography
123
Index of symbols
131
Index
134 |
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| illustrated | Illustrated |
| index_date | 2024-07-02T22:27:02Z |
| indexdate | 2024-07-09T21:23:12Z |
| institution | BVB |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016808075 |
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| physical | 135 S. graph. Darst. |
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| series2 | [Prépublication de l']Institut de Recherche Mathématique Avancée |
| spelling | Salepci, Nermin Verfasser aut Real Lefschetz fibrations par Nermin Salepci Strasbourg IRMA, Univ. Louis Pasteur et C.N.R.S. 2007 135 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier [Prépublication de l']Institut de Recherche Mathématique Avancée 2007,8 Text engl., Einl. franz. Zugl.: Strasbourg, Univ., Diss., 2007 Geometria algébrica real (tese doutorado) larpcal Faserung Mathematik (DE-588)4472884-0 gnd rswk-swf (DE-588)4113937-9 Hochschulschrift gnd-content Faserung Mathematik (DE-588)4472884-0 s DE-604 [Prépublication de l']Institut de Recherche Mathématique Avancée 2007,8 (DE-604)BV008183551 2007,8 Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016808075&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Salepci, Nermin Real Lefschetz fibrations [Prépublication de l']Institut de Recherche Mathématique Avancée Geometria algébrica real (tese doutorado) larpcal Faserung Mathematik (DE-588)4472884-0 gnd |
| subject_GND | (DE-588)4472884-0 (DE-588)4113937-9 |
| title | Real Lefschetz fibrations |
| title_auth | Real Lefschetz fibrations |
| title_exact_search | Real Lefschetz fibrations |
| title_exact_search_txtP | Real Lefschetz fibrations |
| title_full | Real Lefschetz fibrations par Nermin Salepci |
| title_fullStr | Real Lefschetz fibrations par Nermin Salepci |
| title_full_unstemmed | Real Lefschetz fibrations par Nermin Salepci |
| title_short | Real Lefschetz fibrations |
| title_sort | real lefschetz fibrations |
| topic | Geometria algébrica real (tese doutorado) larpcal Faserung Mathematik (DE-588)4472884-0 gnd |
| topic_facet | Geometria algébrica real (tese doutorado) Faserung Mathematik Hochschulschrift |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016808075&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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