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Cohomology of the Moduli Space of Cubic Threefolds and Its Smooth Models
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Cohomology of the Moduli Space of Cubic Threefolds and Its Smooth Models
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eBook
Cohomology of the Moduli Space of Cubic Threefolds and Its Smooth Models
2023
Overview
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.
Publisher
American Mathematical Society
Subject
Algebraic geometry -- (Co)homology theory -- Classical real and complex (co)homology msc
/ Algebraic geometry -- Algebraic groups -- Geometric invariant theory msc
/ Algebraic geometry -- Surfaces and higher-dimensional varieties -- $3$-folds msc
/ Algebraic topology -- Homology and cohomology theories -- Intersection homology and cohomology msc
ISBN
9781470460204, 1470460203
