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Moduli Spaces

In: Enriques Surfaces I

Author

Listed:
  • François Cossec

    (Care of Dyah Rusmiasih)

  • Igor Dolgachev

    (University of Michigan–Ann Arbor, Department of Mathematics)

  • Christian Liedtke

    (Technische Universität München, Zentrum Mathematik - M11)

Abstract

In this chapter, we study the moduli spaces of Enriques surfaces. Over the complex numbers, this can be done via lattice-polarized K3 surfaces and their moduli spaces, which leads to constructions of moduli spaces of marked, unmarked, polarized, and nodal Enriques surfaces. We discuss maps between these moduli spaces and the birational geometry of these moduli spaces, that is, their dimensions, Kodaira dimensions, and (uni-)rationality questions. We study some classical compactifications of some of these moduli spaces, and we address the question whether the boundary itself has a modular interpretation. This leads to the study of Coble surfaces of K3 type and Kulikov degenerations of Enriques surfaces. Finally, we study the moduli spaces in positive and mixed characteristic.

Suggested Citation

  • François Cossec & Igor Dolgachev & Christian Liedtke, 2025. "Moduli Spaces," Springer Books, in: Enriques Surfaces I, edition 0, chapter 0, pages 521-620, Springer.
    • Handle: RePEc:spr:sprchp:978-981-96-1214-7_5
    DOI: 10.1007/978-981-96-1214-7_5
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