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...

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Hauptverfasser: Casalaina-Martin, Sebastian, Grushevsky, Samuel, Hulek, Klaus, Laza, Radu
Format: E-Book Buch
Sprache:Englisch
Veröffentlicht: Providence, Rhode Island American Mathematical Society 2023
Ausgabe:1
Schriftenreihe:Memoirs of the American Mathematical Society
Schlagworte:
Cohomology operations
Moduli theory
Threefolds (Algebraic geometry)
ISBN:9781470460204, 1470460203
ISSN:0065-9266, 1947-6221
Online-Zugang:Volltext
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Beschreibung
Zusammenfassung: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.
Bibliographie: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