Real Enriques Surfaces

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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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.

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

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