Equivariant versal deformations of semistable curves

Jarod Alper; Andrew Kresch

doi:10.1307/mmj/1465329012

Equivariant versal deformations of semistable curves

Jarod Alper, Andrew Kresch

Research output: Contribution to journal › Article › peer-review

12 Citations (Scopus)

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 M_g,n parameterizing n-pointed prestable curves of genus g has an étale neighborhood of [C] isomorphic to the quotient stack [W/Aut(C)].

Original language	English
Pages (from-to)	227-250
Number of pages	24
Journal	Michigan Mathematical Journal
Volume	65
Issue number	2
DOIs	https://doi.org/10.1307/mmj/1465329012
Publication status	Published - Jun 2016

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title = "Equivariant versal deformations of semistable curves",

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 parameterizing n-pointed prestable curves of genus g has an {\'e}tale neighborhood of [C] isomorphic to the quotient stack [W/Aut(C)].",

author = "Jarod Alper and Andrew Kresch",

year = "2016",

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AU - Kresch, Andrew

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N2 - 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 parameterizing n-pointed prestable curves of genus g has an étale neighborhood of [C] isomorphic to the quotient stack [W/Aut(C)].

AB - 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 parameterizing n-pointed prestable curves of genus g has an étale neighborhood of [C] isomorphic to the quotient stack [W/Aut(C)].

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DO - 10.1307/mmj/1465329012

M3 - Article

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VL - 65

SP - 227

EP - 250

JO - Michigan Mathematical Journal

JF - Michigan Mathematical Journal

IS - 2

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Equivariant versal deformations of semistable curves

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