Cohomology of the Moduli Space of Cubic Threefolds and Its Smooth Models Journal Article uri icon



  • 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.

publication date

  • February 1, 2023

has restriction

  • hybrid

Date in CU Experts

  • January 19, 2024 11:43 AM

Full Author List

  • Casalaina-Martin S; Grushevsky S; Hulek K; Laza R

author count

  • 4

Other Profiles

International Standard Serial Number (ISSN)

  • 0065-9266

Electronic International Standard Serial Number (EISSN)

  • 1947-6221

Additional Document Info


  • 282


  • 1395