More reduced obstruction theories

We first develop a general formalism for globally removing factors from a $1$-perfect obstruction theory, analogous to Manetti’s formalism for deformation functors. We then apply this formalism to give a construction of a reduced $1$-perfect obstruction theory on the moduli space of morphisms from a curve to a surface $f : C \to S$ in class $\beta$ such that $H^1(C, f^* T_S) \xrightarrow{-\cup \beta} H^2 (S, \mathcal{O}_S)$ is surjective. This condition appears in recent work of Kool and Thomas.

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Accepted 14 May 2014

Published 13 April 2015