Frobenius manifolds and moduli spaces for singularities:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Cambridge
Cambridge University Press
2002
|
| Edition: | 1. publication |
| Series: | Cambridge Tracts in Mathematics
151 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | IX, 270 Seiten |
| ISBN: | 0521812968 |
Staff View
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Record in the Search Index
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| adam_text | Contents
Preface page viii
Part 1. Multiplication on the tangent bundle
1 Introduction to part 1 3
1.1 First examples 4
1.2 Fast track through the results 5
2 Definition and first properties of F manifolds 9
2.1 Finite dimensional algebras 9
2.2 Vector bundles with multiplication 11
2.3 Definition of F manifolds 14
2.4 Decomposition of F manifolds and examples 16
2.5 F manifolds and potentiality 19
3 Massive F manifolds and Lagrange maps 23
3.1 Lagrange property of massive F manifolds 23
3.2 Existence of Euler fields 26
3.3 Lyashko Looijenga maps and graphs of Lagrange maps 29
3.4 Miniversal Lagrange maps and F manifolds 32
3.5 Lyashko Looijenga map of an F manifold 35
4 Discriminants and modality of F manifolds 40
4.1 Discriminant of an F manifold 40
4.2 2 dimensional F manifolds 44
4.3 Logarithmic vector fields 47
4.4 Isomorphisms and modality of germs of F manifolds 52
4.5 Analytic spectrum embedded differently 56
v
vi Contents
5 Singularities and Coxeter groups 61
5.1 Hypersurface singularities 61
5.2 Boundary singularities 69
5.3 Coxeter groups and F manifolds 75
5.4 Coxeter groups and Frobenius manifolds 82
5.5 3 dimensional and other F manifolds 87
Part 2. Frobenius manifolds, GauB Manin connections, and
moduli spaces for hypersurface singularities
6 Introduction to part 2 99
6.1 Construction of Frobenius manifolds for singularities 100
6.2 Moduli spaces and other applications 104
7 Connections over the punctured plane 109
7.1 Flat vector bundles on the punctured plane 109
7.2 Lattices 113
7.3 Saturated lattices 116
7.4 Riemann Hilbert Birkhoff problem 120
7.5 Spectral numbers globally 128
8 Meromorphic connections 131
8.1 Logarithmic vector fields and differential forms 131
8.2 Logarithmic pole along a smooth divisor 134
8.3 Logarithmic pole along any divisor 139
8.4 Remarks on regular singular connections 143
9 Frobenius manifolds and second structure connections 145
9.1 Definition of Frobenius manifolds 145
9.2 Second structure connections 148
9.3 First structure connections 154
9.4 From the structure connections to metric and multiplication 157
9.5 Massive Frobenius manifolds 160
10 GauB Manin connections for hypersurface singularities 165
10.1 Semiuniversal unfoldings and F manifolds 165
10.2 Cohomology bundle 167
10.3 GauB Manin connection 170
10.4 Higher residue pairings 179
10.5 Polarized mixed Hodge structures and opposite filtrations 183
10.6 Brieskorn lattice 188
Contents vii
11 Frobenius manifolds for hypersurface singularities 195
11.1 Construction of Frobenius manifolds 195
11.2 Deformed flat coordinates 205
11.3 Remarks on mirror symmetry 211
11.4 Remarks on oscillating integrals 212
12 ;ii constant stratum 218
12.1 Canonical complex structure 218
12.2 Period map and infinitesimal Torelli 224
13 Moduli spaces for singularities 230
13.1 Compatibilities 230
13.2 Symmetries of singularities 235
13.3 Global moduli spaces for singularities 240
14 Variance of the spectral numbers 248
14.1 Socle field 248
14.2 G function of a massive Frobenius manifold 251
14.3 Variance of the spectrum 256
Bibliography 260
Index 269
|
| any_adam_object | 1 |
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| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 516 - Geometry |
| dewey-raw | 516.35 |
| dewey-search | 516.35 |
| dewey-sort | 3516.35 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 1. publication |
| format | Book |
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| id | DE-604.BV014315175 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T19:01:34Z |
| institution | BVB |
| isbn | 0521812968 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-009820715 |
| oclc_num | 248171851 |
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| physical | IX, 270 Seiten |
| publishDate | 2002 |
| publishDateSearch | 2002 |
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| publisher | Cambridge University Press |
| record_format | marc |
| series | Cambridge Tracts in Mathematics |
| series2 | Cambridge Tracts in Mathematics |
| spelling | Hertling, Claus Verfasser (DE-588)1161363718 aut Frobenius manifolds and moduli spaces for singularities Claus Hertling 1. publication Cambridge Cambridge University Press 2002 IX, 270 Seiten txt rdacontent n rdamedia nc rdacarrier Cambridge Tracts in Mathematics 151 Frobenius algebras Moduli theory Singularities (Mathematics) Tangentialbündel (DE-588)4236004-3 gnd rswk-swf Frobenius-Mannigfaltigkeit (DE-588)4470001-5 gnd rswk-swf Modulraum (DE-588)4183462-8 gnd rswk-swf Singularität Mathematik (DE-588)4077459-4 gnd rswk-swf Frobenius-Mannigfaltigkeit (DE-588)4470001-5 s Singularität Mathematik (DE-588)4077459-4 s Tangentialbündel (DE-588)4236004-3 s Modulraum (DE-588)4183462-8 s DE-604 Cambridge Tracts in Mathematics 151 (DE-604)BV000000001 151 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009820715&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Hertling, Claus Frobenius manifolds and moduli spaces for singularities Cambridge Tracts in Mathematics Frobenius algebras Moduli theory Singularities (Mathematics) Tangentialbündel (DE-588)4236004-3 gnd Frobenius-Mannigfaltigkeit (DE-588)4470001-5 gnd Modulraum (DE-588)4183462-8 gnd Singularität Mathematik (DE-588)4077459-4 gnd |
| subject_GND | (DE-588)4236004-3 (DE-588)4470001-5 (DE-588)4183462-8 (DE-588)4077459-4 |
| title | Frobenius manifolds and moduli spaces for singularities |
| title_auth | Frobenius manifolds and moduli spaces for singularities |
| title_exact_search | Frobenius manifolds and moduli spaces for singularities |
| title_full | Frobenius manifolds and moduli spaces for singularities Claus Hertling |
| title_fullStr | Frobenius manifolds and moduli spaces for singularities Claus Hertling |
| title_full_unstemmed | Frobenius manifolds and moduli spaces for singularities Claus Hertling |
| title_short | Frobenius manifolds and moduli spaces for singularities |
| title_sort | frobenius manifolds and moduli spaces for singularities |
| topic | Frobenius algebras Moduli theory Singularities (Mathematics) Tangentialbündel (DE-588)4236004-3 gnd Frobenius-Mannigfaltigkeit (DE-588)4470001-5 gnd Modulraum (DE-588)4183462-8 gnd Singularität Mathematik (DE-588)4077459-4 gnd |
| topic_facet | Frobenius algebras Moduli theory Singularities (Mathematics) Tangentialbündel Frobenius-Mannigfaltigkeit Modulraum Singularität Mathematik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009820715&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000000001 |
| work_keys_str_mv | AT hertlingclaus frobeniusmanifoldsandmodulispacesforsingularities |