e-Article
Equivariant Landau-Ginzburg mirror symmetry.
Document Type
Journal
Author
Guéré, Jérémy (F-GREN-IF) AMS Author Profile
Source
Subject
14 Algebraic geometry -- 14N Projective and enumerative geometry
14N35Gromov-Witten invariants, quantum cohomology, Gopakumar-Vafa invariants, Donaldson-Thomas invariants
14N35
Language
English
French
French
Abstract
The paper under review studies equivariant Gromov-Witten theory of hypersurfaces in weighted projective spaces, generalizing the work of A. Chiodo, H. Iritani and Y. Ruan [Publ. Math. Inst. Hautes Études Sci. {\bf 119} (2014), 127--216; MR3210178]. In the framework of the Landau-Ginzburg/Calabi-Yau correspondence, the GW theory of the CY can be understood in terms of the FJRW theory of the associated LG model. In this context, the author computes Hodge-type integrals for the FJRW theory without assuming concavity (in the sense of [A. Chiodo and Y. Ruan, Ann. Inst. Fourier (Grenoble) {\bf 61} (2011), no.~7, 2803--2864; MR3112509]) and using the Atiyah-Bott localization formula.