Cohomology of the moduli space of cubic threefolds and its smooth models / Sebastian Casalaina-Martin, Samuel Grushevsky, Klaus Hulek, Radu Laza.

Author
Casalaina-Martin, Sebastian [Browse]
Format
Book
Language
English
Published/​Created
  • Providence, RI : AMS, American Mathematical Society, 2023.
  • ©2023
Description
v, 100 pages : illustrations ; 26 cm

Details

Subject(s)
Author
Series
Summary note
"We compute and compare the (intersection) cohomology of various natural geometric compactifications of the moduli space of cubic threefolds: the GIT compactification and its Kirwan blowup, as well as the Baily-Borel and toroidal compactifications of the ball quotient model, due to Allcock-Carlson-Toledo. Our starting point is Kirwan's method. We then follow by investigating the behavior of the cohomology under the birational maps relating the various models, using the decomposition theorem in different ways, and via a detailed study of the boundary of the ball quotient model. As an easy illustration of our methods, the simpler case of the moduli space of cubic surfaces is discussed in an appendix."--Page v.
Notes
Number 1395 (fourth of 6 numbers)
Bibliographic references
Includes bibliographical references (pages 97-100).
Contents
  • Chapter 1. Introduction
  • Chapter 2. Preliminaries
  • Chapter 3. The cohomology of the Kirwan blowup, part I
  • Chapter 4. The cohomology of the Kirwan blowup, part II
  • Chapter 5. The intersection cohomology of the GIT moduli space MGIT
  • Chapter 6. The intersection cohomology of the ball quotient
  • Chapter 7. The cohomology of the toroidal compactification
  • Appendix A. Equivariant cohomology
  • Appendix B. Stabilizers, normalizers, and fixed loci for cubic threefolds
  • Appendix C. The moduli space of cubic surfaces
  • Bibliography.
ISBN
  • 9781470460204 ((paperback))
  • 1470460203 ((paperback))
OCLC
1372139230
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