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Mathematische Annalen

, Volume 374, Issue 1–2, pp 1007–1032 | Cite as

Moduli of fibered surface pairs from twisted stable maps

  • Kenneth AscherEmail author
  • Dori Bejleri
Article
  • 45 Downloads

Abstract

In this paper, we use the theory of twisted stable maps to construct compactifications of the moduli space of pairs \((X \rightarrow C, S + F)\) where \(X \rightarrow C\) is a fibered surface, S is a sum of sections, F is a sum of marked fibers, and \((X,S+F)\) is a stable pair in the sense of the minimal model program. This generalizes the work of Abramovich–Vistoli, who compactified the moduli space of fibered surfaces with no marked fibers. Furthermore, we compare our compactification to Alexeev’s space of stable maps and the KSBA compactification. As an application, we describe the boundary of a compactification of the moduli space of elliptic surfaces.

Mathematics Subject Classification

14J10 14D23 

Notes

Acknowledgements

We thank our advisor Dan Abramovich for his constant support. We thank Valery Alexeev, Giovanni Inchiostro, Gabriele La Nave, and Dhruv Ranganathan for helpful suggestions.

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Massachusetts Institute of TechnologyCambridgeUSA
  2. 2.Brown UniversityProvidenceUSA

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