Real Enriques Surfaces

  • Authors
  • Alexander Degtyarev
  • Ilia Itenberg
  • Viatcheslav Kharlamov

Part of the Lecture Notes in Mathematics book series (LNM, volume 1746)

Table of contents

  1. Front Matter
    Pages i-xvi
  2. Alexander Degtyarev, Ilia Itenberg, Viatcheslav Kharlamov
    Pages vii-xiii
  3. Alexander Degtyarev, Ilia Itenberg, Viatcheslav Kharlamov
    Pages 1-28
  4. Alexander Degtyarev, Ilia Itenberg, Viatcheslav Kharlamov
    Pages 29-52
  5. Alexander Degtyarev, Ilia Itenberg, Viatcheslav Kharlamov
    Pages 53-78
  6. Alexander Degtyarev, Ilia Itenberg, Viatcheslav Kharlamov
    Pages 79-87
  7. Alexander Degtyarev, Ilia Itenberg, Viatcheslav Kharlamov
    Pages 88-96
  8. Alexander Degtyarev, Ilia Itenberg, Viatcheslav Kharlamov
    Pages 97-126
  9. Alexander Degtyarev, Ilia Itenberg, Viatcheslav Kharlamov
    Pages 127-144
  10. Alexander Degtyarev, Ilia Itenberg, Viatcheslav Kharlamov
    Pages 145-168
  11. Alexander Degtyarev, Ilia Itenberg, Viatcheslav Kharlamov
    Pages 169-190
  12. Back Matter
    Pages 191-259

About this book

Introduction

This is the first attempt of a systematic study of real Enriques surfaces culminating in their classification up to deformation. Simple explicit topological invariants are elaborated for identifying the deformation classes of real Enriques surfaces. Some of theses are new and can be applied to other classes of surfaces or higher-dimensional varieties. Intended for researchers and graduate students in real algebraic geometry it may also interest others who want to become familiar with the field and its techniques. The study relies on topology of involutions, arithmetics of integral quadratic forms, algebraic geometry of surfaces, and the hyperkähler structure of K3-surfaces. A comprehensive summary of the necessary results and techniques from each of these fields is included. Some results are developed further, e.g., a detailed study of lattices with a pair of commuting involutions and a certain class of rational complex surfaces.

Keywords

Dimension Enriques surfaces Grad algebraic geometry deformation of surfaces hyperkähler structure real algebraic surfaces topology of real algebraic varieties

Bibliographic information

  • DOI https://doi.org/10.1007/BFb0103960
  • Copyright Information Springer-Verlag Berlin Heidelberg 2000
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-41088-1
  • Online ISBN 978-3-540-39948-3
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • About this book