Real Enriques Surfaces

Alexander Degtyarev, Ilia Itenberg, Viatcheslav Kharlamov (auth.)3540410880, 9783540410881

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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Table of contents :
Introduction….Pages vii-xiii
Topology of involutions….Pages 1-28
Integral lattices and quadratic forms….Pages 29-52
Algebraic surfaces….Pages 53-78
Real surfaces: the topological aspects….Pages 79-87
Summary: Deformation Classes….Pages 88-96
Topology of real enriques surfaces….Pages 97-126
Moduli of real enriques surfaces….Pages 127-144
Deformation types: the hyperbolic and parabolic cases….Pages 145-168
Deformation types: the elliptic and parabolic cases….Pages 169-190