The moduli space of cubic threefolds as a ball quotient

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.|The moduli spac...

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Main Authors: Allcock, Daniel, Carlson, James A., Toledo, Domingo
Format: eBook Book
Language:English
Published: Providence, Rhode Island American Mathematical Society 2011
Edition:1
Series:Memoirs of the American Mathematical Society
Subjects:
Moduli theory
Surfaces, Cubic
Threefolds (Algebraic geometry)
moduli space
Ball quotient
period map
cubic threefold
ISBN:0821847511, 9780821847510
ISSN:0065-9266, 1947-6221
Online Access:Get full text
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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. The authors describe both the birational modifications and the discrete group explicitly.|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.
AbstractList 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.|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.
The moduli space of cubic threefolds in
Author Allcock, Daniel
Carlson, James A.
Toledo, Domingo
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  organization: Department of Mathematics, University of Texas at Austin, Austin, Texas 78712
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  givenname: James A.
  surname: Carlson
  fullname: Carlson, James A.
  email: carlson@claymath.org
  organization: Clay Mathematics Institute, One Bow Street, Cambridge, Massachusetts 02138
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  givenname: Domingo
  surname: Toledo
  fullname: Toledo, Domingo
  email: toledo@math.utah.edu
  organization: Department of Mathematics, University of Utah, Salt Lake City, Utah 84112
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Keywords moduli space
Ball quotient
period map
cubic threefold
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Notes Includes bibliographical references (p. 67-68) and index
Volume 209, number 985 (fourth of 5 numbers).
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Snippet The moduli space of cubic threefolds in
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...
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SubjectTerms Moduli theory
Surfaces, Cubic
Threefolds (Algebraic geometry)
TableOfContents Introduction -- 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
Intro -- Contents -- Introduction -- Chapter 1. Moduli of Smooth Cubic Threefolds -- Chapter 2. The Discriminant near a Chordal Cubic -- Chapter 3. Extension of the Period Map -- Chapter 4. Degeneration to a Chordal Cubic -- 4.1. Statement of results -- 4.2. Overview of the calculations -- 4.3. Semistable reduction -- 4.4. Cohomology computations -- Chapter 5. Degeneration to a Nodal Cubic -- Chapter 6. The Main Theorem -- Chapter 7. The Monodromy Group and Hyperplane Arrangement -- Bibliography -- Index
Title The moduli space of cubic threefolds as a ball quotient
URI https://www.ams.org/memo/0985/
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Volume 209
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