The contraction morphism between maps and quasimaps to toric varieties

2024/12/20 by Rabano, Alberto Cobos · 1 citation
#14D20 (Primary) 14M25 #14N35 (Secondary) #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2412.16295

Abstract

Given X a smooth projective toric variety, we construct a morphism from a closed substack of the moduli space of stable maps to X to the moduli space of quasimaps to X. If X is Fano, we show that this morphism is surjective. The construction relies on the notion of degree of a quasimap at a base-point, which we define. We show that a quasimap is determined by its regular extension and the degree of each of its basepoints.

Cited by

• Irreducible components of moduli spaces of maps to smooth projective toric varieties in genus 0

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