Very ample linear series on real algebraic curves (Q2430152)

The study of complete and very ample series on closed Riemann surfaces is known for the case of not very special divisors. On the other hand, for the case of compact Klein surfaces this study is not completely understood. One may think of a compact Klein surface as the quotient space obtained from the action of some anticonformal involution (a symmetry) over a closed Riemann surface. In this way, one may study divisors on a compact Klein surface by studying divisors on a closed Riemann surface which are invariant under some given symmetry. With this in mind, in this article the authors obtain results concerning the existence of complete and very ample divisors on compact bordered Klein surfaces and their relations with the boundary components (the projection of the components of fixed points of the symmetry). As compact Klein surfaces may be seen as real algebraic curves, one may think also of this study as to extend results on complex algebraic curves to the case of real algebraic curves (with non-empty set of real points). In fact, in the article, the authors use the algebraic curve language instead that of Riemann surfaces and Klein surfaces.