DOI: 10.1307/mmj/1465329012
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Abstract: 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)].