2017/07/31 by Mario Kummer, Kristin Shaw · 1 citation
Engineering · Mathematics · #Advanced Numerical Analysis Techniques #Algebraic Geometry and Number Theory #Algebraic curve #Algorithm #Computer science #Embedding #Geometric and Algebraic Topology #Mathematics #Morphism #Projection (relational algebra) #Pure mathematics #Semigroup #math.AG #msc:14H50 #msc:14H51 #msc:14P99
paper · pdf · doi:10.5802/afst.1624
14 pages, 4 figures, published version, comments welcome!
arxiv created 2019/02/07 · openalex publication_date 2020/07/24 · arxiv updated 2020/08/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We introduce the separating semigroup of a real algebraic curve of dividing type. The elements of this semigroup record the possible degrees of the covering maps obtained by restricting separating morphisms to the real part of the curve. We also introduce the hyperbolic semigroup which consists of elements of the separating semigroup arising from morphisms which are compositions of a linear projection with an embedding of the curve to some projective space. We completely determine both semigroups in the case of maximal curves. We also prove that any embedding of a real curve of dividing type to projective space of sufficiently high degree is hyperbolic. Using these semigroups we show that the hyperbolicity locus of an embedded curve is in general not connected.