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Fundamental Factorization of a GLSM Part I: Construction
About this Title
Ionut Ciocan-Fontanine, David Favero, Jérémy Guéré, Bumsig Kim and Mark Shoemaker
Publication: Memoirs of the American Mathematical Society
Publication Year:
2023; Volume 289, Number 1435
ISBNs: 978-1-4704-6543-8 (print); 978-1-4704-7590-1 (online)
DOI: https://doi.org/10.1090/memo/1435
Published electronically: August 23, 2023
Keywords: Gromov–Witten theory,
Fan–Jarvis–Ruan–Witten theory,
matrix factorizations,
Landau–Ginzburg models,
gauged linear sigma model,
virtual cycle,
cosection localization
Table of Contents
Chapters
- 1. Introduction
- 2. Overview of the construction
- 3. Factorizations
- 4. Admissible resolutions of GLSMs
- 5. Construction of a projective embedding
- 6. The GLSM theory for convex hybrid models
- 7. Comparisons with other constructions
Abstract
We define enumerative invariants associated to a hybrid Gauged Linear Sigma Model. We prove that in the relevant special cases these invariants recover both the Gromov–Witten type invariants defined by Chang–Li and Fan–Jarvis–Ruan using cosection localization as well as the FJRW type invariants constructed by Polishchuk–Vaintrob. The invariants are defined by constructing a “fundamental factorization” supported on the moduli space of Landau–Ginzburg maps to a convex hybrid model. This gives the kernel of a Fourier–Mukai transform; the associated map on Hochschild homology defines our theory.- Dima Arinkin, Andrei Căldăraru, and Márton Hablicsek, Formality of derived intersections and the orbifold HKR isomorphism, J. Algebra 540 (2019), 100–120. MR 4003476, DOI 10.1016/j.jalgebra.2019.08.002
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