A TQFT of Intersection Numbers on Moduli Spaces of Admissible Covers

2005/12/11 by Renzo Cavalieri, Cavalieri, Renzo
Computer Science · Engineering · Mathematics · #14N35 #Advanced Numerical Analysis Techniques #Algebraic Geometry (math.AG) #Computational Geometry and Mesh Generation #FOS: Mathematics #Polynomial and algebraic computation #math.AG #msc:14N35

paper · pdf · doi:10.48550/arxiv.math/0512225

arxiv created 2005/12/11 · openalex publication_date 2005/12/11 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We construct a two-level weighted TQFT whose structure coefficents are equivariant intersection numbers on moduli spaces of admissible covers. Such a structure is parallel (and strictly related) to the local Gromov-Witten theory of curves of Bryan-Pandharipande. We compute explicitly the theory using techniques of localization on moduli spaces of admissible covers of a parametrized projective line. The Frobenius Algebras we obtain are one parameter deformations of the class algebra of the symmetric group S_d. In certain special cases we are able to produce explicit closed formulas for such deformations in terms of the representation theory of S_d.

Citations

• Relative virtual localization and vanishing of tautological classes on moduli spaces of curves

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