Real Enriques Surfaces (Lecture Notes in Mathematics)
Edition: 1 edition
Publisher: Springer
Published: November 27, 2000
Language: eng
Format: Paperback
Number of pages: 259
ISBN-13: 9783540410881
Subjects: Algebraic Geometry; Analytic topology; Mathematical Analysis; Mathematics; Science/Mathematics; General; Geometry - Algebraic; 14J15; 14J28; 14J80; 14P25; 15J50; 57S17; 58D27; Mathematics / Geometry / Algebraic; deformation of surfaces; hyperkähler structure; real algebraic surfaces; Enriques surfaces
First sentence: In this chapter we give a brief overview of some basic results on topology of involutions, both classical (Smith theory, Lefschetz fixed point formula, and signature formula) and relatively new (Kalinin's spectral sequence).
Description: 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.