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The Moduli Space of Cubic Threefolds as a Ball Quotient
Daniel Allcock, University of Texas at Austin, TX, and James A. Carlson and Domingo Toledo, University of Utah, Salt Lake City, UT

Memoirs of the American Mathematical Society
2011; 70 pp; softcover
Volume: 209
ISBN-10: 0-8218-4751-1
ISBN-13: 978-0-8218-4751-0
List Price: US$70
Individual Members: US$42
Institutional Members: US$56
Order Code: MEMO/209/985
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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. The authors describe both the birational modifications and the discrete group explicitly.

Table of Contents

  • Moduli of smooth cubic threefolds
  • The discriminant near a chordal cubic
  • Extension of the period map
  • Degeneration to a chordal cubic
  • Degeneration to a nodal cubic
  • The Main theorem
  • The monodromy group and hyperplane arrangement
  • Bibliography
  • Index
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