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010 a| 2023013006;

020 a| 9781470460204q| (paperback);

020 z| 9781470473518q| (pdf);

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100 1 a| Casalaina-Martin, Sebastian.?| UNAUTHORIZED;

245 10 a| Cohomology of the moduli space of cubic threefolds and its smooth modelsh| [electronic resource] /c| Sebastian Casalaina-Martin, Samuel Grushevsky, Klaus Hulek, Radu Laza.;

260 a| Providence, RI :b| AMS, American Mathematical Society,c| 2023.;

300 a| v, 100 pages :b| illustrations ;c| 26 cm.;

490 0 a| Memoir of the American Methematical Society,x| 0065-9266 ;v| volume 282, number 1395;

504 a| Includes bibliographical references (pages 97-100).;

505 0 a| 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.;

506 a| Available only to authorized users.;

520 a| "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"--c| Provided by publisher.;

538 a| Mode of access: World Wide Web;

650 0 a| Cohomology operations.=| ^A512842;

650 0 a| Moduli theory.=| ^A121775;

650 0 a| Threefolds (Algebraic geometry)=| ^A364570;

650 7 a| Algebraic geometry -- Surfaces and higher-dimensional varieties -- $3$-folds.2| msc;

650 7 a| Algebraic geometry -- Surfaces and higher-dimensional varieties -- Families, moduli, classification: algebraic theory.2| msc;

650 7 a| Algebraic geometry -- Algebraic groups -- Geometric invariant theory.2| msc;

650 7 a| Algebraic geometry -- (Co)homology theory -- Classical real and complex (co)homology.2| msc;

650 7 a| Algebraic topology -- Homology and cohomology theories -- Intersection homology and cohomology.2| msc;

650 7 a| Algebraic topology -- Homology and cohomology theories -- Homology with local coefficients, equivariant cohomology.2| msc;

655 0 a| Electronic books.=| ^A491897;

700 1 a| Grushevsky, Samuel.?| UNAUTHORIZED;

700 1 a| Hulek, Klaus.=| ^A288861;

700 1 a| Laza, Radu.=| ^A1286922;

856 40 z| Full text available from Ebook Central - Academic Completeu| https://ebookcentral.proquest.com/lib/eastcarolina/detail.action?docID=30404201;

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Cohomology of the moduli space of cubic threefolds and its smooth models / Sebastian Casalaina-Martin, Samuel Grushevsky, Klaus Hulek, Radu Laza.

Author/creator	Casalaina-Martin, Sebastian
Other author	Grushevsky, Samuel.
Other author	Hulek, Klaus.
Other author	Laza, Radu.
Format	Electronic
Publication Info	Providence, RI : AMS, American Mathematical Society, 2023.
Description	v, 100 pages : illustrations ; 26 cm.
Supplemental Content	Full text available from Ebook Central - Academic Complete
Subjects	Cohomology operations. Moduli theory. Threefolds (Algebraic geometry)

Series	Memoir of the American Methematical Society, 0065-9266 ; volume 282, number 1395
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.
Abstract	"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"-- Provided by publisher.
Bibliography note	Includes bibliographical references (pages 97-100).
Access restriction	Available only to authorized users.
Technical details	Mode of access: World Wide Web
Genre/form	Electronic books.
LCCN	2023013006
ISBN	9781470460204 (paperback)
ISBN	(pdf)

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Cohomology of the moduli space of cubic threefolds and its smooth models / Sebastian Casalaina-Martin, Samuel Grushevsky, Klaus Hulek, Radu Laza.

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