Hodge integrals in FJRW theory
J\'er\'emy Gu\'er\'e
TL;DR
This paper provides a universal formula for computing certain intersection numbers in higher genus FJRW theory for chain polynomials, expanding computational tools in algebraic geometry.
Contribution
It introduces an explicit method to compute the cup product of the virtual class with the top Chern class of the Hodge bundle in any genus, without semi-simplicity assumptions.
Findings
Derived a formula valid in all genera
Applicable to any chain polynomial and symmetry group
No semi-simplicity assumption required
Abstract
We study higher genus Fan--Jarvis--Ruan--Witten theory of any chain polynomial with any group of symmetries. Precisely, we give an explicit way to compute the cup product of Polishchuk and Vaintrob's virtual class with the top Chern class of the Hodge bundle. Our formula for this product holds in any genus and without any assumption on the semi-simplicity of the underlying cohomological field theory.
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Algebraic structures and combinatorial models · Advanced Algebra and Geometry