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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| Hlavní autoři: | , , , |
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| Médium: | E-kniha Kniha |
| Jazyk: | angličtina |
| Vydáno: |
Providence, Rhode Island
American Mathematical Society
2023
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| Vydání: | 1 |
| Edice: | Memoirs of the American Mathematical Society |
| Témata: | |
| ISBN: | 9781470460204, 1470460203 |
| ISSN: | 0065-9266, 1947-6221 |
| On-line přístup: | Získat plný text |
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| Shrnutí: | 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. |
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| Bibliografie: | 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 |