Pencils on separating (M-2)-curves

2012/06/14 by Marc Coppens, Coppens, Marc
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Geometric and Algebraic Topology #math.AG

paper · pdf · doi:10.48550/arxiv.1206.3016

15 pages

arxiv created 2012/06/14 · arxiv updated 2012/06/15

Abstract

A separating (M-2)-curve is a smooth geometrically irreducible real projective curve X such that X(ℝ) has g-1 connected components and X(ℂ)∖ X(ℝ) is disconnected. Let T_g be a Teichmüller space of separating (M-2)-curves of genus g. We consider two partitions of T_g, one by means of a concept of special type, the other one by means of the separating gonality. We show that those two partitions are very closely related to each other. As an application we obtain the existence of real curves having isolated real linear systems g¹_g-1 for all g≥ 4.

Related

• Real plane separating (M-2)-curves of degree d and totally real pencils of degree d-3
• The separating gonality of a separating real curve
• Obstructions for the existence of separating morphisms and totally real pencils
• Separating semigroup of genus 4 curves
• Separating semigroup of hyperelliptic curves and of genus 3 curves