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Compactifying Moduli Spaces

This book focusses on a large class of objects in moduli theory and provides different perspectives from which compactifications of moduli spaces may be investigated. Three contributions give an insight on particular aspects of moduli problems. In the first of them, various ways to construct and com...

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Main Authors: Hacking, Paul. (Author, http://id.loc.gov/vocabulary/relators/aut), Laza, Radu. (http://id.loc.gov/vocabulary/relators/aut), Oprea, Dragos. (http://id.loc.gov/vocabulary/relators/aut)
Corporate Author: SpringerLink (Online service)
Other Authors: Bini, Gilberto. (Editor, http://id.loc.gov/vocabulary/relators/edt), Lahoz, Martí. (Editor, http://id.loc.gov/vocabulary/relators/edt), Macrí, Emanuele. (Editor, http://id.loc.gov/vocabulary/relators/edt), Stellari, Paolo. (Editor, http://id.loc.gov/vocabulary/relators/edt)
Language:English
Published: Basel : Springer Basel : Imprint: Birkhäuser, 2016.
Edition:1st ed. 2016.
Series:Advanced Courses in Mathematics - CRM Barcelona,
Subjects:
Algebraic geometry.
Algebraic Geometry.
Online Access:https://doi.org/10.1007/978-3-0348-0921-4
Table of Contents:
  • Foreword
  • 1: Perspectives on moduli spaces
  • The GIT Approach to constructing moduli spaces
  • Moduli and periods
  • The KSBA approach to moduli spaces
  • Bibliography
  • 2: Compact moduli of surfaces and vector bundles
  • Moduli spaces of surfaces of general type
  • Wahl singularities
  • Examples of degenerations of Wahl type
  • Exceptional vector bundles associated to Wahl degenerations
  • Examples
  • Bibliography
  • 3: Notes on the moduli space of stable quotients
  • Morphism spaces and Quot schemes over a fixed curve
  • Stable quotients
  • Stable quotient invariants
  • Wall-crossing and other geometries
  • Bibliography.

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