Details

Subject(s)

• Cohomology operations [Browse]
• Moduli theory [Browse]

Author

• Grushevsky, Samuel [Browse]
• Hulek, Klaus [Browse]
• Laza, Radu [Browse]

Series

• Memoirs of the American Mathematical Society ; no. 1395. [More in this series]
• Memoirs of the American Mathematical Society, 0065-9266 ; number 1395 [More in this 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.

Show 8 more Contents items

ISBN

• 9781470460204 ((paperback))
• 1470460203 ((paperback))

OCLC

1372139230

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