Totally real theta characteristics
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A totally real theta characteristic of a real curve is a theta characteristic which is linearly equivalent to a sum of only real points. These are closely related to the facets of the convex hull of the canonical embedding of the curve. We give upper and lower bounds for the number of both of totally real theta characteristics and facets.
KeywordsReal algebraic curves Theta characteristics Convex algebraic geometry
Mathematics Subject ClassificationPrimary 14P99 14H40
I would like to thank all the participants of the “Tritangent Summit” that took place at the Max Planck Institute for Mathematics in the Sciences in Leipzig in January 2018. Furthermore, I want to thank the diligent referee who pointed out some inaccuracies and gaps and even helped to eliminate them.
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