Year: 2023
Type: preprint
Abstract: The theory of Mixed-Spin-P (MSP) fields was introduced by Chang-Li-Li-Liu for the quintic threefold, aiming at studying its higher-genus Gromov-Witten invariants. Chang-Guo-Li has successfully applied it to prove conjectures including the BCOV Feynman rule, Yamaguchi-Yau's polynomiality conjecture and the Holomorphic Anomaly Equation. Meanwhile, Fan-Jarvis-Ruan introduced a mathematical theory of Gauged Linear Sigma Model (GLSM), associating a counting theory to a GIT quotient with a super-potential, under suitable assumptions. This paper provides a common generalization of both works, by introducing new stability conditions in the mathematical GLSM. We show that our stability condition guarantees the separatedness and properness of the cosection degeneracy locus in the moduli. It generalizes the MSP fields construction to more general GIT quotients, including Calabi-Yau global complete intersections in toric varieties. This hopefully provides a geometric platform to effectively compute their higher-genus Gromov-Witten invariants.
Source: arXiv (Cornell University)
Authors: Chang, Huai-Liang, Guo, Shuai, Li, Jun, Li, Wei-Ping, Zhou, Yang
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4390040998