Abstract. We prove that given any n-pointed prestable curve C of genus g with linearly reductive automorphism group Aut(C), there exists an Aut(C)-equivariant miniversal deformation of C over an affine variety W . In other words, we prove that the algebraic stack Mg,n parametrizing n-pointed prestable curves of genus g has anétale neighborhood of [C] isomorphic to the quotient stack [W/ Aut(C)].
scite is a Brooklyn-based startup that helps researchers better discover and evaluate scientific articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by researchers from dozens of countries and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.