Tropical geometry and mirror symmetry:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Providence, R.I.
Amer. Math. Soc.
2011
|
| Series: | Regional conference series in mathematics
114 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturverz.: S. 307 - 311 |
| Physical Description: | XVI, 317 S. graph. Darst. |
| ISBN: | 9780821852323 0821852329 |
Staff View
MARC
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| 100 | 1 | |a Gross, Mark |d 1965- |e Verfasser |0 (DE-588)124077846 |4 aut | |
| 245 | 1 | 0 | |a Tropical geometry and mirror symmetry |c Mark Gross |
| 264 | 1 | |a Providence, R.I. |b Amer. Math. Soc. |c 2011 | |
| 300 | |a XVI, 317 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Regional conference series in mathematics |v 114 | |
| 500 | |a Literaturverz.: S. 307 - 311 | ||
| 650 | 4 | |a Tropical geometry | |
| 650 | 4 | |a Mirror symmetry | |
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| 650 | 0 | 7 | |a Spiegelsymmetrie |0 (DE-588)4538605-5 |2 gnd |9 rswk-swf |
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Record in the Search Index
| _version_ | 1804145618628640768 |
|---|---|
| adam_text | Contents
Preface
ix
Introduction
xi
Part
1.
The three worlds I
Chapter
1.
The tropics
3
1.1.
Tropical hypersurfaces
3
1.2.
Some background on fans
11
1.3.
Parameterized tropical curves
13
1.4.
Affine
manifolds with singularities
19
1.5.
The discrete Legendre transform
27
1.6.
Tropical curves on tropical surfaces
30
1.7.
References and further reading
32
Chapter
2.
The A- and B-models
33
2.1.
The A-model
33
2.2.
The B-model
67
2.3.
References and further reading
89
Chapter
3.
Log geometry
91
3.1.
A brief review of toric geometry
92
3.2.
Log schemes
98
3.3.
Log derivations and differentials
112
3.4.
Log deformation theory
117
3.5.
The twisted
de Rham
complex revisited
126
3.6.
References and further reading
129
Part
2.
Example: P2.
131
Chapter
4.
Mikhalkin s curve counting formula
133
4.1.
The statement and outline of the proof
133
4.2.
Log world
—»
tropical world
138
4.3.
Tropical world
->
log world
143
4.4.
Classical world
-»
log world
157
4.5.
Log world
—»
classical world
165
4.6.
The end of the proof
169
4.7.
References and further reading
171
Chapter
5.
Period integrals
173
5.1.
The perturbed Landau-Ginzburg potential
173
viii CONTENTS
5.2.
Tropical descendent
invariants
179
5.3.
The main B-model statement
187
5.4.
Deforming
Q
and
ΡΎ,
...,
Pk
192
5.5.
Evaluation of the period integrals
222
5.6.
References and further reading
244
Part
3.
The Gross-Siebert program
245
Chapter
6.
The program and two-dimensional results
247
6.1.
The program
247
6.2.
From integral tropical manifolds to degenerations in dimension two
255
6.3.
Achieving compatibility: The tropical vertex group
290
6.4.
Remarks and generalizations
305
6.5.
References and further reading
306
Bibliography
307
Index of Symbols
313
General Index
315
|
| any_adam_object | 1 |
| author | Gross, Mark 1965- |
| author_GND | (DE-588)124077846 |
| author_facet | Gross, Mark 1965- |
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| bvnumber | BV037334691 |
| callnumber-first | Q - Science |
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| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 200 SK 350 SK 240 |
| ctrlnum | (OCoLC)712399537 (DE-599)BVBBV037334691 |
| dewey-full | 516.3/5 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 516 - Geometry |
| dewey-raw | 516.3/5 |
| dewey-search | 516.3/5 |
| dewey-sort | 3516.3 15 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV037334691 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T23:22:19Z |
| institution | BVB |
| isbn | 9780821852323 0821852329 |
| language | English |
| lccn | 2010043384 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-022488527 |
| oclc_num | 712399537 |
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| owner | DE-188 DE-355 DE-BY-UBR DE-11 DE-739 DE-83 |
| owner_facet | DE-188 DE-355 DE-BY-UBR DE-11 DE-739 DE-83 |
| physical | XVI, 317 S. graph. Darst. |
| publishDate | 2011 |
| publishDateSearch | 2011 |
| publishDateSort | 2011 |
| publisher | Amer. Math. Soc. |
| record_format | marc |
| series | Regional conference series in mathematics |
| series2 | Regional conference series in mathematics |
| spelling | Gross, Mark 1965- Verfasser (DE-588)124077846 aut Tropical geometry and mirror symmetry Mark Gross Providence, R.I. Amer. Math. Soc. 2011 XVI, 317 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Regional conference series in mathematics 114 Literaturverz.: S. 307 - 311 Tropical geometry Mirror symmetry Tropische Geometrie (DE-588)7566380-6 gnd rswk-swf Spiegelsymmetrie (DE-588)4538605-5 gnd rswk-swf Tropische Geometrie (DE-588)7566380-6 s Spiegelsymmetrie (DE-588)4538605-5 s DE-604 Regional conference series in mathematics 114 (DE-604)BV000004346 114 Digitalisierung UB Passau application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=022488527&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Gross, Mark 1965- Tropical geometry and mirror symmetry Regional conference series in mathematics Tropical geometry Mirror symmetry Tropische Geometrie (DE-588)7566380-6 gnd Spiegelsymmetrie (DE-588)4538605-5 gnd |
| subject_GND | (DE-588)7566380-6 (DE-588)4538605-5 |
| title | Tropical geometry and mirror symmetry |
| title_auth | Tropical geometry and mirror symmetry |
| title_exact_search | Tropical geometry and mirror symmetry |
| title_full | Tropical geometry and mirror symmetry Mark Gross |
| title_fullStr | Tropical geometry and mirror symmetry Mark Gross |
| title_full_unstemmed | Tropical geometry and mirror symmetry Mark Gross |
| title_short | Tropical geometry and mirror symmetry |
| title_sort | tropical geometry and mirror symmetry |
| topic | Tropical geometry Mirror symmetry Tropische Geometrie (DE-588)7566380-6 gnd Spiegelsymmetrie (DE-588)4538605-5 gnd |
| topic_facet | Tropical geometry Mirror symmetry Tropische Geometrie Spiegelsymmetrie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=022488527&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000004346 |
| work_keys_str_mv | AT grossmark tropicalgeometryandmirrorsymmetry |