Twisted stable maps with colliding points
Martin Olsson, Rachel Webb
TL;DR
This paper explores the moduli spaces of stable maps from pointed curves with colliding points into tame Deligne-Mumford stacks, extending existing theories of twisted stable maps and weighted pointed curves.
Contribution
It generalizes the Abramovich-Vistoli theory to include colliding points and broadens the framework to maps into tame Deligne-Mumford stacks.
Findings
Developed a new moduli space framework for colliding points
Extended twisted stable map theory to more general stacks
Connected to previous work on weighted pointed curves
Abstract
We study moduli spaces of stable maps from pointed curves, where the points are allowed to coincide, with target a tame Deligne-Mumford stack. This generalizes the Abramovich-Vistoli theory of twisted stable maps as well as work of Hassett, Alexeev and Guy, and Bayer and Manin, who studied stable maps to projective varieties from curves with weighted marked points.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Geometry and complex manifolds · Homotopy and Cohomology in Algebraic Topology