Lagrangian floer theory and mirror symmetry on compact toric manifolds:
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| Main Authors: | , , , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Paris
Société Mathématique de France
2016
|
| Series: | Astérisque
376 |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028874812&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Physical Description: | vi, 340 Seiten Illustrationen |
| ISBN: | 9782856298251 |
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MARC
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| 245 | 1 | 0 | |a Lagrangian floer theory and mirror symmetry on compact toric manifolds |c Kenji Fukaya, Yong-Geun Oh, Hiroshi Ohta & Kaoru Ono |
| 264 | 1 | |a Paris |b Société Mathématique de France |c 2016 | |
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| 700 | 1 | |a Fukaya, Kenji |d 1959- |0 (DE-588)142815144 |4 aut | |
| 700 | 1 | |a Oh, Yong-Geun |d 1961- |0 (DE-588)1079551433 |4 aut | |
| 700 | 1 | |a Ohta, Hiroshi |d 1949- |0 (DE-588)1145604021 |4 aut | |
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Record in the Search Index
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| adam_text | Titel: Lagrangian Floer theory and mirror symmetry on compact toric manifolds
Autor: Kenji, Fukaya
Jahr: 2016
CONTENTS 1. Introduction ........................................................... 1 1.1. Introduction ........................................................ 1 1.2. Notations and terminologies ........................................ 9 1.3. Statement of the results ............................................. 11 1.4. Projective space: an example ....................................... 26 2. Ring isomorphism .................................................... 29 2.1. Norms and completions of polynomial ring over Novikov ring ....... 29 2.2. Localization of Jacobian ring at moment polytope .................. 33 2.3. Operator q: review .................................................. 37 2.4. Well-definedness of Kodaira-Spencer map ........................... 46 2.5. Well-definedness of potential function ............................... 59 2.6. Kodaira-Spencer map is a ring homomorphism ...................... 64 2.7. Surjectivity of Kodaira-Spencer map ................................ 86 2.8. Versality of the potential function with bulk ........................ 90 2.9. Algebraization of Jacobian ring ..................................... 92 2.10. Seidel homomorphism and a result by MeDuff-Tolman ............. 97 2.11. Injectivity of Kodaira-Spencer map ................................ 101 2.11.1. The case b G 7?(A + ) ........................................... 101 2.11.2. The case b G iT(A 0 ) ........................................... 117 2.12. The Chern class rj and critical values of tpO b ..................... 124 2.13. Hirzebruch surface Fp an example ................................ 126 3. Coincidence of pairings ............................................... 131 3.1. Operator p and Poincare duality .................................... 131 3.2. Cyclic symmetry in the toric cast ................................... 137 3.3. Operator p in the toric case ......................................... 117 3.4.
Moduli space of holouiorphic annuli ................................. 15 1 3.5. Poincaré dualily is residue pairing .................................. 179 3.6. Clifford algebra and Hessian matrix ................................. 181 3.7. Residue pairing anil Hessian determinant ........................... 185 3.8. Cyclic homology and variat ion of the invariant Z ................... 190 3.9. Orientation ......................................................... 205 3.9.1. Operators D i and D .......................................... 206 1 I h MAI llKMA?Mj??. OK KHANCK jn 1 ;
( ( )NTKNTS vi 13.9.2. ( )ri( ]it al jon of I ndex I )i ........................................ 207 15.4.1). Orientât ion of Index !)? ........................................ 20!) . 5.0.1. ( oui inuat iun of linear Kuranishi models ........................ 210 ; i. lu. S i ” 11 in 1 1 icori M 11 :l,l.l and Proposition 15.0.2 ....................... 2113 15.10.1. Sonic Icnmiata ................................................ 214 13.10.2. Prools ol signs in Theorem 13.4.1 ami Proposition 13.7).2 ........ 218 4. Appendix .............................................................. 227 1.1. ( oineidenee of thè Imi définitions ol ............................ 227 1.2. Interpolation lietweeu Kuranishi st met ures ......................... 22!) 1.15. 7 e |iiivariant and cyclically synimel rie Knranislii st met uri s ....... 2134 1.15.1. 1 lie case of une disk coinponent I .............................. 241 1.13.2. 1 lie case of onc disk eoinponent H ............................. 2513 1.15.15. The case of une disk eoniponent III ............................. 25!) 1.15.1. The rase of more ! l s .................... 207 1.15.5. Ta k i 11 o the sinn ol olisi met ion spaees so t ha 1 coordinate change exisls ......................................................... 275 1 .15. fi. lakin o filier produci with T invariant cycles .................. 280 1.1. Continuons Inmilv ol 7 equivariant and cyclic svinine! rie muli iseel ions ...................... ................................. 282 1.5, (’onstmetion of varions ollier Kuranishi st. met mes.................. 284 1.5.1. (’oust met ion ol p-kuraiiishi si met ure .......................... 284 1.5.2. (’onstmetion ol t-Kuranishi slnieture .......................... 28!) 1.5. H Prool of I. emina 1.2.7 .......................................... 291 1.5.1. Kuranishi struci ure on I he moduli spaee of psoudo-holoniorphio annuii I
...................................................... 297 1.5.5. Knranislii si met uri- on t lie moduli space ol pseudodioloniorphic annuii 11 ...................................................... 1501 1.5. li. Kuranishi sinici ure on thè moduli spaee of pseudo-holomorphic annuii III ..................................................... 1)0!) 1.5. Piool ol Temimi 2.5.27 .............................................. li 14 1.7. 11 1 ) i 1 1 s e 1 1 i I d and quant um cohomologies .............................. 1520 Hibliography .............................................................. 151)15 Index ...................................................................... 1)159
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| any_adam_object | 1 |
| author | Fukaya, Kenji 1959- Oh, Yong-Geun 1961- Ohta, Hiroshi 1949- Ono, Kaoru 1962- |
| author_GND | (DE-588)142815144 (DE-588)1079551433 (DE-588)1145604021 (DE-588)1196732485 |
| author_facet | Fukaya, Kenji 1959- Oh, Yong-Geun 1961- Ohta, Hiroshi 1949- Ono, Kaoru 1962- |
| author_role | aut aut aut aut |
| author_sort | Fukaya, Kenji 1959- |
| author_variant | k f kf y g o ygo h o ho k o ko |
| building | Verbundindex |
| bvnumber | BV043457517 |
| classification_rvk | SK 370 SI 832 |
| ctrlnum | (OCoLC)941400810 (DE-599)BSZ457054727 |
| discipline | Mathematik |
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| id | DE-604.BV043457517 |
| illustrated | Illustrated |
| indexdate | 2024-12-20T17:36:53Z |
| institution | BVB |
| isbn | 9782856298251 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-028874812 |
| oclc_num | 941400810 |
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| owner_facet | DE-384 DE-29T DE-19 DE-BY-UBM DE-355 DE-BY-UBR DE-188 |
| physical | vi, 340 Seiten Illustrationen |
| publishDate | 2016 |
| publishDateSearch | 2016 |
| publishDateSort | 2016 |
| publisher | Société Mathématique de France |
| record_format | marc |
| series | Astérisque |
| series2 | Astérisque |
| spellingShingle | Fukaya, Kenji 1959- Oh, Yong-Geun 1961- Ohta, Hiroshi 1949- Ono, Kaoru 1962- Lagrangian floer theory and mirror symmetry on compact toric manifolds Astérisque |
| title | Lagrangian floer theory and mirror symmetry on compact toric manifolds |
| title_auth | Lagrangian floer theory and mirror symmetry on compact toric manifolds |
| title_exact_search | Lagrangian floer theory and mirror symmetry on compact toric manifolds |
| title_full | Lagrangian floer theory and mirror symmetry on compact toric manifolds Kenji Fukaya, Yong-Geun Oh, Hiroshi Ohta & Kaoru Ono |
| title_fullStr | Lagrangian floer theory and mirror symmetry on compact toric manifolds Kenji Fukaya, Yong-Geun Oh, Hiroshi Ohta & Kaoru Ono |
| title_full_unstemmed | Lagrangian floer theory and mirror symmetry on compact toric manifolds Kenji Fukaya, Yong-Geun Oh, Hiroshi Ohta & Kaoru Ono |
| title_short | Lagrangian floer theory and mirror symmetry on compact toric manifolds |
| title_sort | lagrangian floer theory and mirror symmetry on compact toric manifolds |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028874812&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV002579439 |
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