The geometry of cubic hypersurfaces / Daniel Huybrechts.

Format:

Book

Author/Creator:

Huybrechts, Daniel, author.

Series:

Cambridge studies in advanced mathematics ; 206.

Language:

English

Subjects (All):

Surfaces, Cubic.

Hypersurfaces.

Equations, Cubic.

Geometry, Algebraic.

Physical Description:

1 online resource (xvii, 441 pages) : digital, PDF file(s).

Place of Publication:

Cambridge ; New York, NY : Cambridge University Press, 2023.

Summary:

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.

Contents:

Basic facts

Fano varieties of lines

Moduli spaces

Cubic surfaces

Cubic threefolds

Cubic fourfolds

Derived categories of cubic hypersurfaces.

Notes:

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

Other Format:

Print version:

ISBN:

9781009280020 (ebook)

Access Restriction:

Restricted for use by site license.