Moduli of curves on toric varieties and their stable cohomology

2022/10/11 by Banerjee, Oishee
#Algebraic Geometry (math.AG) #Algebraic Topology (math.AT) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2210.05826

Abstract

We prove that the cohomology of the moduli space of morphisms of a fixed finite degree from a smooth projective curve C of genus g to a complete simplicial toric variety ℙ(Σ), denoted by the rational polyhedral fan Σ, stabilizes. As an arithmetic consequence we obtain a resolution of the Batyrev-Manin conjecture for toric varieties over global function fields in all but finitely many characteristics.

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