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

Research output: Book/Report › Monograph › Research

Authors

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

Research Organisations

External Research Organisations

  • University of Colorado Boulder
  • Ruder Boskovic Institute
  • Stony Brook University (SBU)
  • Princeton University
View graph of relations

Details

Original languageEnglish
Number of pages112
Volume282
Edition1395
ISBN (electronic)978-1-4704-7351-8
Publication statusPublished - Feb 2023

Publication series

NameMemoirs of the American Mathematical Society
PublisherAmerican Mathematical Society
No.1395
Volume282
ISSN (Print)0065-9266

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.

Keywords

    math.AG, 14J30, 14J10, 14L24, 14F25, 55N33, 55N25

ASJC Scopus subject areas

Cite this

Cohomology of the moduli space of cubic threefolds and its smooth models. / Hulek, Klaus; Casalaina-Martin, Sebastian; Laza, Radu et al.
1395 ed. 2023. 112 p. (Memoirs of the American Mathematical Society; Vol. 282, No. 1395).

Research output: Book/Report › Monograph › Research

Hulek, K, Casalaina-Martin, S, Laza, R & Grushevsky, S 2023, Cohomology of the moduli space of cubic threefolds and its smooth models. Memoirs of the American Mathematical Society, no. 1395, vol. 282, vol. 282, 1395 edn. https://doi.org/10.1090/memo/1395
Hulek, K., Casalaina-Martin, S., Laza, R., & Grushevsky, S. (2023). Cohomology of the moduli space of cubic threefolds and its smooth models. (1395 ed.) (Memoirs of the American Mathematical Society; Vol. 282, No. 1395). https://doi.org/10.1090/memo/1395
Hulek K, Casalaina-Martin S, Laza R, Grushevsky S. Cohomology of the moduli space of cubic threefolds and its smooth models. 1395 ed. 2023. 112 p. (Memoirs of the American Mathematical Society; 1395). Epub 2023 Jan 3. doi: 10.1090/memo/1395
Hulek, Klaus ; Casalaina-Martin, Sebastian ; Laza, Radu et al. / Cohomology of the moduli space of cubic threefolds and its smooth models. 1395 ed. 2023. 112 p. (Memoirs of the American Mathematical Society; 1395).
Download
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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{\textquoteright}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.",
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note = "Funding Information: Research of the first author is supported in part by grants from the Simons Foundation (317572) and the NSA (H98230-16-1-0053). Research of the second author is supported in part by NSF grants DMS-15-01265 and DMS-18-02116. Research of the third author is supported in part by DFG grant Hu-337/7-1. Research of the fourth author is supported in part by NSF grants DMS-12-54812 and DMS-18-02128. The first author would like to thank the Institut f{\"u}r Algebraische Geometrie at Leibniz Universit{\"a}t for support during the Fall Semester 2017. The first and third authors are also grateful to MSRI Berkeley, which is supported by NSF Grant DMS-14-40140, for providing excellent working conditions in the Spring Semester 2019.",
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