Equivariant versal deformations of semistable curves

2015/10/12 by Jarod Alper, Alper, Jarod, Andrew Kresch +1
Mathematics · #Algebraic Geometry (math.AG) #FOS: Mathematics #math.AG

paper · pdf · doi:10.48550/arxiv.1510.03201

21 pages

arxiv created 2015/10/12 · arxiv updated 2015/10/13

Abstract

We prove that given any n-pointed prestable curve C of genus g with linearly reductive automorphism group \rm Aut(C), there exists an \rm Aut(C)-equivariant miniversal deformation of C over an affine variety W. In other words, we prove that the algebraic stack \mathfrakM_g,n parametrizing n-pointed prestable curves of genus g has an étale neighborhood of [C] isomorphic to the quotient stack [W / \rm Aut(C)].

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