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

Format:

Book

Author/Creator:

Casalaina-Martin, Sebastian, author.

Grushevsky, Samuel, author.

Hulek, Klaus, author.

Laza, Radu, author.

Series:

Memoirs of the American Mathematical Society ; no. 1395.

Memoirs of the American Mathematical Society, 0065-9266 ; number 1395

Language:

English

Subjects (All):

Cohomology operations.

Moduli theory.

Threefolds (Algebraic geometry).

Physical Description:

v, 100 pages : illustrations ; 26 cm.

Place of Publication:

Providence, RI : AMS, American Mathematical Society, 2023.

Summary:

"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"-- Provided by publisher.

Contents:

Preliminaries

The cohomology of the Kirwan blowup, part I : equivariant cohomology of the semi-stable locus

The cohomology of the Kirwan blowup, part II

The intersection cohomology of the GIT moduli space MGIT

The intersection cohomology of the ball quotient

The cohomology of the toroidal compactification.

Notes:

Includes bibliographical references (pages 97-100).

ISBN:

9781470460204

1470460203

OCLC:

1372139230