Cohomology of the moduli space of cubic threefolds and its smooth models

authored by

Klaus Hulek, Sebastian Casalaina-Martin, Radu Laza, Samuel Grushevsky

Abstract

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.

Organisation(s)

Institut für Algebraische Geometrie

External Organisation(s)

University of Colorado Boulder
Ruder Boskovic Institute
Stony Brook University (SBU)
Princeton University

Type

Monografie

Volume

282

No. of pages

112

Publication date

02.2023

Publication status

Veröffentlicht

ASJC Scopus Sachgebiete

Angewandte Mathematik, Mathematik (insg.)

Electronic version(s)

https://arxiv.org/abs/1904.08728 (Access: Offen)
https://doi.org/10.1090/memo/1395 (Access: Geschlossen)