Non-special divisors on real algebraic curves and embeddings into real projective spaces. (English) Zbl 1072.14072
It is proved that on a given real algebraic curve \(X\) there is a large class of non-special divisors of relatively small degree, and if \(X\) has many real components, such a divisor determines an embedding of \(X\) into the real projective space \(\mathbb{P}^r\) for \(r\geq 3\) (and a birational embedding for \(r=2\)). These embeddings are then studied in detail.
Reviewer: Vladimir L. Popov (Moskva)
MSC:
14P05 | Real algebraic sets |
14C20 | Divisors, linear systems, invertible sheaves |
14H50 | Plane and space curves |
14P25 | Topology of real algebraic varieties |