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Mathematische Zeitschrift

, Volume 276, Issue 1–2, pp 299–328 | Cite as

Moduli spaces of hyperelliptic curves with A and D singularities

  • Maksym FedorchukEmail author
Article

Abstract

We introduce moduli spaces of quasi-admissible hyperelliptic covers with at worst A and D singularities. The stability conditions for these moduli spaces depend on two rational parameters describing allowable singularities. For the extreme values of the parameters, we obtain the stacks of stable limits of \(A_n\) and \(D_n\) singularities, and the quotients of the miniversal deformation spaces of these singularities by natural \(\mathbb G _m\)-actions. We interpret the intermediate spaces as log canonical models of the stacks of stable limits of \(A_n\) and \(D_n\) singularities.

Keywords

Moduli stacks Moduli of curves Singularities  Log minimal model program 

Mathematics Subject Classification (2000)

Primary 14D23 Secondary 14H20 14B07 

Notes

Acknowledgments

The whole project was motivated by a question asked by Brendan Hassett to whom we are especially grateful. We had numerous helpful discussions related to the content of this paper with Jarod Alper, Aise Johan de Jong, and David Smyth. We thank Sebastian Casalaina-Martin and Radu Laza for sharing an early version of [9]. We also thank the referee whose suggestions significantly improved the exposition.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.Department of MathematicsColumbia UniversityNew YorkUSA
  2. 2.Department of MathematicsBoston CollegeChestnut HillUSA

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