Lagrangian Floer theory and Mirror symmetry on compact toric manifolds / Kenji Fukaya, Yong-Geun Oh, Hiroshi Ohta,...[et al.]
Type de document : MonographieCollection : Astérisque, 376Langue : anglais.Pays: France.Éditeur : Paris : Société Mathématique de France, 2016Description : 1 vol. (vi+340 p.) ; 24 cmISBN: 9782856298251.ISSN: 0303-1179.Bibliographie : Bibliogr. p. 333-338, index.Sujet MSC : 53D37, Differential geometry - Symplectic geometry, contact geometry, Symplectic aspects of mirror symmetry, homological mirror symmetry, and Fukaya category53D40, Differential geometry - Symplectic geometry, contact geometry, Symplectic aspects of Floer homology and cohomology
53D45, Differential geometry - Symplectic geometry, contact geometry, Gromov-Witten invariants, quantum cohomology, Frobenius manifolds
14B07, Local theory in algebraic geometry, Deformations of singularities
14M25, Algebraic geometry - Special varieties, Toric varieties, Newton polyhedra, Okounkov bodiesEn-ligne : Texte intégral
| Item type | Current library | Call number | Status | Date due | Barcode |
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Monographie
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CMI Salle 1 | Séries SMF 376 (Browse shelf(Opens below)) | Available | 08887-01 |
Bibliogr. p. 333-338, index
In this volume we study Lagrangian Floer theory on toric manifolds from the point of view of mirror symmetry. We construct a natural isomorphism between the Frobenius manifold structures of the (big) quantum cohomology of the toric manifold and of Saito's theory of singularities of the potential function constructed in [Fukaya, Tohoku Math. J. 63 (2011)] via the Floer cohomology deformed by ambient cycles. Our proof of the isomorphism involves the open-closed Gromov-Witten theory of one-loop. (SMF)
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