Hurwitz-Hodge Integrals, the E6 and D4 root systems, and the Crepant Resolution Conjecture

2007/08/30 by Jim Bryan, Bryan, Jim, Amin Gholampour +1 · 1 citation
Computer Science · Mathematics · #14H10 #14N35 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.0708.4244

openalex publication_date 2007/08/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let G be the group A₄ or Z₂xZ₂. We compute the integral of λ_g on the Hurwitz locus H_G⊂ M_g of curves admitting a degree 4 cover of P¹ having monodromy group G. We compute the generating functions for these integrals and write them as a trigonometric expression summed over the positive roots of the E₆ and D₄ root systems respectively. As an application, we prove the Crepant Resolution Conjecture for the orbifolds [C³/A₄] and [C³/(Z₂xZ₂)].

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