Witten’s top Chern class on the moduli space of higher spin curves

By Alexander Polishchuk. 2002

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This paper is a sequel to [9]. Its goal is to verify that the virtual top Chern class c 1/r in the Chow group of the moduli space of higher spin curves \(\overline M _{{g,n}}^{{1/r}} \) constructed in [9], satisfies all the axioms of spin virtual class formulated in [5]. Hence, according to [5], it gives rise to a cohomological field theory in the sense of Kontsevich-Manin [7]. As was observed in [9], the only non-trivial axioms that have to be checked for the class c 1/r are two axioms that we call Vanishing axiom and Ramond factorization axiom. The first of them requires c 1/r to vanish on all the components of the moduli space \(\overline M _{{g,n}}^{{1/r}} \) where one of the markings is equal to r - 1. The second demands vanishing of the push-forward of c 1/r restricted to the components of the moduli space corresponding to the so called Ramond sector, under some natural finite maps.

Subfields: Computational Theory and Mathematics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/e8948e198d975af09834247a084b60942c9f91e4

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Citations in the corpus

The Witten equation, mirror symmetry and quantum singularity theory (2007, methodology): “1] has been constructed for the twisted sectors (often called narrow sectors) by Polishchuk and Vaintrob [Pol04], [PV01].”
Landau–Ginzburg/Calabi–Yau correspondence for quintic three-folds via symplectic transformations (2008, unknown): “1.1 (for the A-singularity case see [2, 5, 25, 26, 35, 36 ]).”