Cohomology of the Moduli Space of Cubic Threefolds and Its Smooth Models

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–To...

Full description

Saved in:
Bibliographic Details
Main Authors: Casalaina-Martin, Sebastian, Grushevsky, Samuel, Hulek, Klaus, Laza, Radu
Format: eBook Book
Language:English
Published: Providence, Rhode Island American Mathematical Society 2023
Edition:1
Series:Memoirs of the American Mathematical Society
Subjects:
Cohomology operations
Moduli theory
Threefolds (Algebraic geometry)
ISBN:9781470460204, 1470460203
ISSN:0065-9266, 1947-6221
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
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.
Bibliography:Other authors: Samuel Grushevsky, Klaus Hulek, Radu Laza
February 2023, volume 282, number 1395 (fourth of 6 numbers)
Includes bibliographical references (p. 97-100)
ISBN:9781470460204
1470460203
ISSN:0065-9266
1947-6221
DOI:10.1090/memo/1395