Skip to content
Register Sign in Wishlist

Lectures on K3 Surfaces

$60.00 USD

Part of Cambridge Studies in Advanced Mathematics

  • Date Published: September 2016
  • availability: This ISBN is for an eBook version which is distributed on our behalf by a third party.
  • format: Adobe eBook Reader
  • isbn: 9781316797570

$ 60.00 USD
Adobe eBook Reader

You will be taken to ebooks.com for this purchase
Buy eBook Add to wishlist

Other available formats:
Hardback


Looking for an inspection copy?

This title is not currently available on inspection

Description
Product filter button
Description
Contents
Resources
Courses
About the Authors
  • 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.

    • Includes many proofs and applies techniques from diverse areas
    • Suitable for coursework or as a reference for researchers
    • Provides opportunities for further research
    Read more

    Reviews & endorsements

    '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

    'This book will be extremely valuable to all mathematicians who are interested in K3 surfaces and related topics. It not only serves as an excellent introduction, but also covers a wide variety of advanced subjects, ranging from complex geometry to derived geometry and arithmetic.' Klaus Hulek, Leibniz Universität Hannover

    'Since the nineteenth century, K3 surfaces have been a source of intriguing examples, problems and theorems. Huybrechts' book is a beautiful and reader-friendly presentation of the main results regarding this special class of varieties. The author fully succeeded in illustrating the richness of concepts and techniques which come into play in the theory of K3 surfaces.' Kieran G. O'Grady, Università degli Studi di Roma 'La Sapienza', Italy

    'K3 surfaces play a ubiquitous role in algebraic geometry. At first glance they seem to be well understood and easy to describe, still they provide non-trivial examples of the most fundamental concepts: Hodge structures, moduli spaces, Chow ring, vector bundles, Picard and Brauer groups … Huybrechts' book, written with the usual talent of the author, is the first to cover systematically all these aspects. It will be an invaluable reference for algebraic geometers.' Arnaud Beauville, Université de Nice, Sophia Antipolis

    '… the book covers many subjects and recent developments, and contains an encyclopedic total of 655 references, which will be very useful for researchers and graduate students. A reader who opens any page of the book will enjoy the subject there. This book will become one's favorite book.' Shigeyuki Kondo, MathSciNet

    'The book is a welcome addition to the literature, especially since its scope ranges from a very good introduction to K3 surfaces to the more recent advances on these surfaces and related topics.' Felipe Zaldivar, MAA Reviews

    See more reviews

    Customer reviews

    Not yet reviewed

    Be the first to review

    Review was not posted due to profanity

    ×

    , create a review

    (If you're not , sign out)

    Please enter the right captcha value
    Please enter a star rating.
    Your review must be a minimum of 12 words.

    How do you rate this item?

    ×

    Product details

    • Date Published: September 2016
    • format: Adobe eBook Reader
    • isbn: 9781316797570
    • contains: 21 b/w illus.
    • availability: This ISBN is for an eBook version which is distributed on our behalf by a third party.
  • Table of Contents

    Preface
    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.

  • Author

    Daniel Huybrechts, University of Bonn
    Daniel Huybrechts is a professor at the Mathematical Institute of the University of Bonn. He previously held positions at the Université Denis Diderot Paris 7 and the University of Cologne. He is interested in algebraic geometry, particularly special geometries with rich algebraic, analytic, and arithmetic structures. His current work focuses on K3 surfaces and higher dimensional analogues. He has published four books.

Sign In

Please sign in to access your account

Cancel

Not already registered? Create an account now. ×

Sorry, this resource is locked

Please register or sign in to request access. If you are having problems accessing these resources please email lecturers@cambridge.org

Register Sign in
Please note that this file is password protected. You will be asked to input your password on the next screen.

» Proceed

You are now leaving the Cambridge University Press website. Your eBook purchase and download will be completed by our partner www.ebooks.com. Please see the permission section of the www.ebooks.com catalogue page for details of the print & copy limits on our eBooks.

Continue ×

Continue ×

Continue ×

Find content that relates to you

Join us online

This site uses cookies to improve your experience. Read more Close

Are you sure you want to delete your account?

This cannot be undone.

Cancel

Thank you for your feedback which will help us improve our service.

If you requested a response, we will make sure to get back to you shortly.

×
Please fill in the required fields in your feedback submission.
×