Higher genus curves on toric varieties

TL;DR

This paper studies the space of morphisms from a smooth projective curve to a toric variety, providing a compactification and analyzing its intersection theory to understand geometric properties.

Contribution

It introduces a new compactification of the morphism space from curves to toric varieties and investigates its intersection theory, advancing understanding of these moduli spaces.

Findings

Constructed a compactification of the morphism space

Analyzed intersection theory on the compactified space

Provided insights into the geometry of morphisms to toric varieties

Abstract

Given a smooth and projective curve C and a smooth and projective toric variety X, we first describe a compactification of the space of morphisms from C to X representing a fixed homology class, and after we study the intersection theory on this variety.