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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
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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$66
Individual Members: US$39.60
Institutional Members: US$52.80
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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