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2007•Pacific Journal of MathematicsOpen access

Anisotropic real curves and bordered line arrangements

Johannes Huisman, Michele Lattarulo

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Abstract

A real curve X of genus g ≥ 2 is anisotropic if the image of the canonical morphism k : X → ‫ސ‬ g-1 is a rational real curve having no real points.We describe the moduli space of anisotropic curves, proving that it is isomorphic to the moduli space of double coverings of ‫ސ‬ 2 ramified along real line arrangements.

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A real curve X of genus g ≥ 2 is anisotropic if the image of the canonical morphism k : X → ‫ސ‬ g-1 is a rational real curve having no real points.We describe the moduli space of anisotropic curves, proving that it is isomorphic to the moduli space of double coverings of ‫ސ‬ 2 ramified along real line arrangements.

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Available abstract

A real curve X of genus g ≥ 2 is anisotropic if the image of the canonical morphism k : X → ‫ސ‬ g-1 is a rational real curve having no real points.We describe the moduli space of anisotropic curves, proving that it is isomorphic to the moduli space of double coverings of ‫ސ‬ 2 ramified along real line arrangements.

Key concepts: Mathematics, Algebraic curve, Projective line, Real projective plane, Projective space, Hyperelliptic curve, Combinatorics, Geometry

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