Derived moduli of sections and push-forwards

TL;DR

This paper introduces a derived enhancement of the moduli space of sections, computes its tangent complex, and applies it to prove the equality of G-theoretic stable map and quasi-map invariants for projective spaces.

Contribution

It develops a derived version of the moduli space of sections and demonstrates its utility in comparing different types of invariants.

Findings

Derived moduli space of sections is constructed and analyzed.

Tangent complex of the derived moduli space is explicitly computed.

G-theoretic stable map and quasi-map invariants of projective spaces are shown to be equal.

Abstract

We introduce a derived enhancement of the moduli space of sections defined by Chang-Li, and we compute its tangent complex. Special cases of this moduli space include stable maps and stable quasi-maps. As an application, we prove that G-theoretic stable map and quasi-map invariants of projective spaces are equal.