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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-Carl...

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Bibliographic Details
Main Authors: Casalaina-Martin, Sebastian (Author)
Group Author: Grushevsky, Samuel; Hulek, Klaus; Laza, Radu
Published: American Mathematical Society,
Publisher Address: Providence, RI :
Publication Dates: 2023.
Literature type: Book
Language: English
Series: Memoirs of the American Mathematical Society, volume 282, number 1395 (fourth of 6 numbers)
Subjects:
Cohomology operations.
Moduli theory.
Threefolds (Algebraic geometry)
Summary: "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"--
Carrier Form: v, 100 pages : illustrations ; 26 cm.
Bibliography: Includes bibliographical references (pages 97-100).
ISBN: 9781470460204
1470460203
Index Number: QA169
CLC: O189.22
Call Number: O189.22/C334
Contents: Preliminaries -- The cohomology of the Kirwan blowup, part I : equivariant cohomology of the semi-stable locus -- The cohomology of the Kirwan blowup, part II -- The intersection cohomology of the GIT moduli space MGIT -- The intersection cohomology of the ball quotient -- The cohomology of the toroidal compactification.

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