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The Weierstrass semigroup of a pair and moduli in $$\mathcal {M}_3$$. (English) Zbl 1077.14534
Summary: We classify all the Weierstrass semigroups of a pair of points on a curve of genus 3, by using its canonical model in the plane. Moreover, we count the dimension of the moduli of curves which have a pair of points with a specified Weierstrass semigroup.

##### MSC:
 14H55 Riemann surfaces; Weierstrass points; gap sequences 14H10 Families, moduli of curves (algebraic) 14H45 Special algebraic curves and curves of low genus 14H50 Plane and space curves
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##### References:
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