REAL HYPERELLIPTIC SURFACES AND THE ORBIFOLD FUNDAMENTAL GROUP

Abstract

In this paper we finish the topological classification of real algebraic surfaces of Kodaira dimension zero and we make a step towards the Enriques classification of real algebraic surfaces, by describing in detail the structure of the moduli space of real hyperelliptic surfaces.Moreover, we point out the relevance in real geometry of the notion of the orbifold fundamental group of a real variety, and we discuss related questions on real varieties is a is a real hyperelliptic surface, then the differentiable type of the pair , and to prove that they are exactly 78.It follows also as a corollary that there are exactly eleven cases for the topological type of the real part of corresponding to a real hyperelliptic surface, the corresponding moduli space is irreducible (and connected).We also give, through a series of tables, explicit analytic representations of the 78 components of the moduli space.AMS 2000 Mathematics subject classification: Primary 14P99; 14P25; 14J15; 32Q57