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Cambridge Studies in Advanced Mathematics Ser.: Lectures on K3 Surfaces by Daniel Huybrechts (2016, Hardcover)
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About this product
Product Identifiers
PublisherCambridge University Press
ISBN-101107153042
ISBN-139781107153042
eBay Product ID (ePID)222051718
Product Key Features
Number of Pages496 Pages
Publication NameLectures on K3 Surfaces
LanguageEnglish
SubjectAlgebra / General, Topology, Geometry / Algebraic
Publication Year2016
TypeTextbook
Subject AreaMathematics
AuthorDaniel Huybrechts
SeriesCambridge Studies in Advanced Mathematics Ser.
FormatHardcover
Dimensions
Item Height1.3 in
Item Weight29 Oz
Item Length9.2 in
Item Width6.2 in
Additional Product Features
Intended AudienceScholarly & Professional
LCCN2016-019204
Dewey Edition23
Reviews"K3 surfaces play something of a magical role in algebraic geometry and neighboring areas. They arise in astonishingly varied contexts, and the study of K3 surfaces has propelled the development of many of the most powerful tools in the field. The present lectures provide a comprehensive and wide-ranging survey of this fascinating subject. Suitable both for study and as a reference work, and written with Huybrechts's usual clarity of exposition, this book is destined to become the standard text on K3 surfaces." Rob Lazarsfeld, State University of New York, Stony Brook
Series Volume NumberSeries Number 158
IllustratedYes
Dewey Decimal516.352
Table Of ContentPreface; 1. Basic definitions; 2. Linear systems; 3. Hodge structures; 4. Kuga-Satake construction; 5. Moduli spaces of polarised K3 surfaces; 6. Periods; 7. Surjectivity of the period map and Global Torelli; 8. Ample cone and Kähler cone; 9. Vector bundles on K3 surfaces; 10. Moduli spaces of sheaves on K3 surfaces; 11. Elliptic K3 surfaces; 12. Chow ring and Grothendieck group; 13. Rational curves on K3 surfaces; 14. Lattices; 15. Automorphisms; 16. Derived categories; 17. Picard group; 18. Brauer group.
SynopsisK3 surfaces are central objects in mathematics and connect to string theory in physics. By studying the many rich aspects of these surfaces, this book surveys powerful techniques in algebraic geometry. Working from the basics to recent breakthroughs, it is suitable as a graduate text and reference for researchers., 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.
LC Classification NumberQA571.H89 2016
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