Moduli of stable maps with fields
Renata Picciotto

TL;DR
This paper constructs a new moduli space of stable maps with fields linked to a variety, a bundle, and a section, generalizing the Quantum Lefschetz principle and relating to existing comparison results.
Contribution
It introduces a novel moduli space framework for stable maps with fields, extending the Quantum Lefschetz principle and providing a new approach to comparison theorems.
Findings
The class matches the virtual fundamental class up to a sign.
The construction generalizes the Quantum Lefschetz hyperplane principle.
Provides a different method from previous comparison results.
Abstract
We construct a moduli space of stable maps with fields associated to a triple of a projective variety (or a DM stack with projective moduli space) a vector bundle and a section. We show the class coincides up to a sign with the virtual fundamental class on the moduli space of stable maps to . We show that this gives a generalization of the Quantum Lefschetz hyperplane principle. This generalizes similar comparison results of Chang--Li, Kim--Oh and Chang--Li and presents a different approach from Chen--Janda--Webb.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Geometry and complex manifolds · Homotopy and Cohomology in Algebraic Topology
