The Evaluation Space of Logarithmic Stable Maps

TL;DR

This paper constructs the evaluation space for minimal logarithmic stable maps, enabling the development of logarithmic Gromov-Witten theory for log-smooth schemes, advancing the understanding of enumerative geometry in logarithmic settings.

Contribution

It introduces the evaluation stack for minimal logarithmic stable maps, providing foundational tools for logarithmic Gromov-Witten theory in log-smooth schemes.

Findings

Construction of the evaluation stack for minimal log stable maps

Definition of evaluation maps for logarithmic Gromov-Witten invariants

Establishment of logarithmic Gromov-Witten theory for log-smooth schemes

Abstract

The evaluation stack for minimal logarithmic stable maps is constructed, parameterizing families of standard log points in the target log scheme. This construction provides the ingredients necessary to define appropriate evaluation maps for minimal log stable maps and establish the logarithmic Gromov-Witten theory of a log-smooth Deligne- Faltings log scheme.