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MiS Preprint

The separating semigroup of a real curve

Mario Denis Kummer and Kristin Shaw


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 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.


Related publications

2020 Repository Open Access
Mario Kummer and Kristin Shaw

The separating semigroup of a real curve

In: Annales de la Faculté des Sciences de Toulouse, 29 (2020) 1, pp. 79-96