Title: Cohomology of the Moduli Space of Cubic Threefolds and Its Smooth Models (Memoirs of the American Mathematical Society, 1395)
Publisher: Amer Mathematical Society
Publication Date: 2023
Language: English
ISBN 10: 1470460203
ISBN 13: 9781470460204
Binding: Soft cover
Condition: New

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Synopsis

"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 theball 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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