Oleg Viro
Published 2006-11-13Version 1
We study natural additional structures on real algebraic surfaces with trivial first homology mod 2 of the complexification. If the set of real points realizes the zero of the second homology mod 2 of the complexification, then the set of real points is equipped with a pair of opposite orientations and a Spin structure. If the set of real points realizes the same homology class as the complexification of a real curve on the surface, then the complement of the curve in set of real points is equipped a pair of opposite orientations, which do not extend across the curve, and the whole set of real points is equipped with a Pin^- structure. These constructions are similar to the complex orientations of real algebraic curves dividing their complexifications and generalize to high dimensions.
Journal: Advances in Soviet Math., vol. 18, 1994, 261-284
Overview of topological properties of real algebraic surfaces
Nonnegativity certificates on real algebraic surfaces
Real algebraic surfaces with many handles in $(\mathbb{CP}^1)^3$
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