The moduli space of cubic threefolds as a ball quotient / Daniel Allcock, James A. Carlson, Domingo Toledo.

Format:

Book

Author/Creator:

Allcock, Daniel, 1969- author.

Carlson, James A., 1946- author.

Toledo, Domingo, author.

Series:

Memoirs of the American Mathematical Society ; Volume 209, Number 985.

Memoirs of the American Mathematical Society, 0065-9266 ; Volume 209, Number 985

Language:

English

Subjects (All):

Moduli theory.

Surfaces, Cubic.

Threefolds (Algebraic geometry).

Physical Description:

1 online resource (70 p.)

Edition:

1st ed.

Place of Publication:

Providence, Rhode Island : American Mathematical Society, 2010.

Language Note:

English

Summary:

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.

Contents:

""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""

Notes:

"Volume 209, Number 985 (fourth of 5 numbers)."

Includes bibliographical references and index.

Description based on print version record.

ISBN:

1-4704-0599-7