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Real Enriques Surfaces

  • Book
  • © 2000

Overview

Authors:
  1. Alexander Degtyarev
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  2. Ilia Itenberg
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  3. Viatcheslav Kharlamov
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Part of the book series: Lecture Notes in Mathematics (LNM, volume 1746)

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Table of contents (10 chapters)

  1. Front Matter

    Pages i-xvi
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  2. Introduction

    • Alexander Degtyarev, Ilia Itenberg, Viatcheslav Kharlamov
    Pages vii-xiii

  3. Topology of involutions

    • Alexander Degtyarev, Ilia Itenberg, Viatcheslav Kharlamov
    Pages 1-28

  4. Integral lattices and quadratic forms

    • Alexander Degtyarev, Ilia Itenberg, Viatcheslav Kharlamov
    Pages 29-52

  5. Algebraic surfaces

    • Alexander Degtyarev, Ilia Itenberg, Viatcheslav Kharlamov
    Pages 53-78

  6. Real surfaces: the topological aspects

    • Alexander Degtyarev, Ilia Itenberg, Viatcheslav Kharlamov
    Pages 79-87

  7. Summary: Deformation Classes

    • Alexander Degtyarev, Ilia Itenberg, Viatcheslav Kharlamov
    Pages 88-96

  8. Topology of real enriques surfaces

    • Alexander Degtyarev, Ilia Itenberg, Viatcheslav Kharlamov
    Pages 97-126

  9. Moduli of real enriques surfaces

    • Alexander Degtyarev, Ilia Itenberg, Viatcheslav Kharlamov
    Pages 127-144

  10. Deformation types: the hyperbolic and parabolic cases

    • Alexander Degtyarev, Ilia Itenberg, Viatcheslav Kharlamov
    Pages 145-168

  11. Deformation types: the elliptic and parabolic cases

    • Alexander Degtyarev, Ilia Itenberg, Viatcheslav Kharlamov
    Pages 169-190

  12. Back Matter

    Pages 191-259
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Keywords

About this book

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.

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