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Lectures on K3 Surfaces 1st Edition by Daniel Huybrechts ISBN 1107153042 9781107153042

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Lectures on K3 Surfaces 1st Edition Daniel Huybrechts Digital Instant Download

Author(s): Daniel Huybrechts
ISBN(s): 9781107153042, 1107153042
Edition: 1
File Details: PDF, 2.39 MB
Year: 2016
Language: english
SKU: EB-7036482 Category: Tag:

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Product details:

ISBN 10: 1107153042

ISBN 13: 9781107153042 

Author: Daniel Huybrechts 

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 facets of K3 surfaces, including arithmetic, homological, and differential geometric aspects. In this context, the book covers Hodge structures, moduli spaces, periods, derived categories, birational techniques, Chow rings, and deformation theory. Famous open conjectures, for example the conjectures of Calabi, Weil, and Artin-Tate, are discussed in general and for K3 surfaces in particular, and each chapter ends with questions and open problems. Based on lectures at the advanced graduate level, this book is suitable for courses and as a reference for researchers.

Table of contents:

  1. Linear Systems

  2. Hodge Structures

  3. KugaSatake Construction

  4. Moduli Spaces of Polarized K3 Surfaces

  5. Periods

  6. Surjectivity of the Period Map and Global Torelli

  7. Ample Cone and Kähler Cone

  8. Vector Bundles on K3 Surfaces

  9. Moduli Spaces of Sheaves on K3 Surfaces

  10. Elliptic K3 Surfaces

  11. Chow Ring and Grothendieck Group

  12. Rational Curves on K3 Surfaces

  13. Lattices

  14. Automorphisms

  15. Derived Categories

  16. Picard Group

  17. Brauer Group

  18. References

  19. Index

  20. List of Notation

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Tags: Daniel Huybrechts, Lectures, K3, Surfaces