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The geometry of cubic hypersurfaces

Record Type:	Electronic resources : Monograph/item
Title/Author:	The geometry of cubic hypersurfacesDaniel Huybrechts.
Author:	Huybrechts, Daniel.
Published:	Cambridge ;Cambridge University Press,2023.
Description:	xvii, 441 p. :ill., digital ;24 cm.
Notes:	Title from publisher's bibliographic system (viewed on 15 Jun 2023).
Subject:	Surfaces, Cubic.
Online resource:	https://doi.org/10.1017/9781009280020
ISBN:	9781009280020$q(electronic bk.)

The geometry of cubic hypersurfaces
Huybrechts, Daniel.

The geometry of cubic hypersurfaces[electronic resource] /Daniel Huybrechts. - Cambridge ;Cambridge University Press,2023. - xvii, 441 p. :ill., digital ;24 cm. - Cambridge studies in advanced mathematics ;206.. - Cambridge studies in advanced mathematics ;105..

Title from publisher's bibliographic system (viewed on 15 Jun 2023).

Basic facts -- Fano varieties of lines -- Moduli spaces -- Cubic surfaces -- Cubic threefolds -- Cubic fourfolds -- Derived categories of cubic hypersurfaces.

Cubic hypersurfaces are described by almost the simplest possible polynomial equations, yet their behaviour is rich enough to demonstrate many of the central challenges in algebraic geometry. With exercises and detailed references to the wider literature, this thorough text introduces cubic hypersurfaces and all the techniques needed to study them. The book starts by laying the foundations for the study of cubic hypersurfaces and of many other algebraic varieties, covering cohomology and Hodge theory of hypersurfaces, moduli spaces of those and Fano varieties of linear subspaces contained in hypersurfaces. The next three chapters examine the general machinery applied to cubic hypersurfaces of dimension two, three, and four. Finally, the author looks at cubic hypersurfaces from a categorical point of view and describes motivic features. Based on the author's lecture courses, this is an ideal text for graduate students as well as an invaluable reference for researchers in algebraic geometry.

ISBN: 9781009280020$q(electronic bk.)Subjects--Topical Terms:

662250
Surfaces, Cubic.

LC Class. No.: QA573 / .H89 2023

Dewey Class. No.: 516.352

The geometry of cubic hypersurfaces
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245 1 4 $a The geometry of cubic hypersurfaces $h [electronic resource] / $c Daniel Huybrechts.
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300 $a xvii, 441 p. : $b ill., digital ; $c 24 cm.
490 1 $a Cambridge studies in advanced mathematics ; $v 206.
500 $a Title from publisher's bibliographic system (viewed on 15 Jun 2023).
505 0 $a Basic facts -- Fano varieties of lines -- Moduli spaces -- Cubic surfaces -- Cubic threefolds -- Cubic fourfolds -- Derived categories of cubic hypersurfaces.
520 $a Cubic hypersurfaces are described by almost the simplest possible polynomial equations, yet their behaviour is rich enough to demonstrate many of the central challenges in algebraic geometry. With exercises and detailed references to the wider literature, this thorough text introduces cubic hypersurfaces and all the techniques needed to study them. The book starts by laying the foundations for the study of cubic hypersurfaces and of many other algebraic varieties, covering cohomology and Hodge theory of hypersurfaces, moduli spaces of those and Fano varieties of linear subspaces contained in hypersurfaces. The next three chapters examine the general machinery applied to cubic hypersurfaces of dimension two, three, and four. Finally, the author looks at cubic hypersurfaces from a categorical point of view and describes motivic features. Based on the author's lecture courses, this is an ideal text for graduate students as well as an invaluable reference for researchers in algebraic geometry.
650 0 $a Surfaces, Cubic. $3 662250
650 0 $a Hypersurfaces. $3 511758
650 0 $a Equations, Cubic. $3 715927
650 0 $a Geometry, Algebraic $v Textbooks. $3 438731
830 0 $a Cambridge studies in advanced mathematics ; $v 105. $3 541725
856 4 0 $u https://doi.org/10.1017/9781009280020