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The moduli space of cubic threefolds as a ball quotient

About this Title

Daniel Allcock, Department of Mathematics, University of Texas at Austin, Austin, Texas 78712, James A. Carlson, Department of Mathematics, University of Utah, Salt Lake City, Utah 84112 and Domingo Toledo, Department of Mathematics, University of Utah, Salt Lake City, Utah 84112

Publication: Memoirs of the American Mathematical Society
Publication Year: 2011; Volume 209, Number 985
ISBNs: 978-0-8218-4751-0 (print); 978-1-4704-0599-1 (online)
DOI: https://doi.org/10.1090/S0065-9266-10-00591-0
Published electronically: July 15, 2010
Keywords: Ball quotient, period map, moduli space, cubic threefold
MSC: Primary 32G20; Secondary 14J30

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Table of Contents

Chapters

  • Introduction
  • 1. Moduli of Smooth Cubic Threefolds
  • 2. The Discriminant near a Chordal Cubic
  • 3. Extension of the Period Map
  • 4. Degeneration to a Chordal Cubic
  • 5. Degeneration to a Nodal Cubic
  • 6. The Main Theorem
  • 7. The Monodromy Group and Hyperplane Arrangement

Abstract

The moduli space of cubic threefolds in $\mathbb {C}P^4$, with some minor birational modifications, is the Baily-Borel compactification of the quotient of the complex 10-ball by a discrete group. We describe both the birational modifications and the discrete group explicitly.

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