More Reduced Obstruction Theories

TL;DR

This paper introduces a formalism for simplifying obstruction theories globally and applies it to construct a reduced obstruction theory for moduli of maps from curves to surfaces under specific conditions.

Contribution

It develops a general method to remove factors from obstruction theories and applies it to a particular moduli problem, extending previous work by Kool and Thomas.

Findings

Constructed a reduced obstruction theory for certain moduli spaces

Provided a formalism for globally removing factors from obstruction theories

Extended the understanding of obstruction theories in algebraic geometry

Abstract

This short note first develops a general formalism for globally removing a factor from an obstruction theory. This formalism is then applied to give a construction of a reduced obstruction theory on the moduli of maps from a curve to a surface satisfying a technical condition. This condition was recently identified in work of Kool and Thomas.