Very Twisted Stable Maps

TL;DR

This paper introduces the moduli stack of very twisted stable maps, extending existing theories to include generic stabilizers on source curves, and explores its implications for Gromov-Witten theory.

Contribution

It extends the concept of twisted stable maps to include generic stabilizers, broadening the scope of Gromov-Witten theory for Deligne-Mumford stacks.

Findings

Construction of the moduli stack of very twisted stable maps

Extension of Gromov-Witten theory to this new setting

Framework for studying stable maps with generic stabilizers

Abstract

Let X be a smooth projective Deligne-Mumford stack over an algebraically closed field k of characteristic 0. In this paper we construct the moduli stack of very twisted stable maps, extending the notion of twisted stable maps by Abramovich and Vistoli to allow for generic stabilizers on the source curves. We also consider the Gromov-Witten theory given by this construction.