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Lectures on K3 surfaces

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"K3 surfaces are central objects in modern algebraic geometry. This book examines this important class of Calabi-Yau manifolds from various perspectives in eighteen self-contained chapters. It starts with the basics and guides the reader to recent breakthroughs, such as the proof of the Tate conjecture for K3 surfaces and structural results on Chow groups. Powerful general techniques are introduced to study the many  Read more...

Author(s): Huybrechts, Daniel
Series: Cambridge studies in advanced mathematics 158.
Publisher: Cambridge University Press
Year: 2016

Language: English
Pages: 485
Tags: Surfaces, Algebraic;Threefolds (Algebraic geometry);Geometry, Algebraic

Basic definitions --
Linear systems --
Hodge structures --
Kuga-Satake construction --
Moduli spaces of polarized K3 surfaces --
Periods --
Surjectivity of the period map and global Torelli --
Ample cone and Kähler Cone --
Vector bundles on K3 surfaces --
Moduli spaces of sheaves on K3 surfaces --
Elliptic K3 surfaces --
Chow ring and Grothendieck group --
Rational curves on K3 surfaces --
Lattices --
Automorphisms --
Derived categories --
Picard group --
Brauer group.