On the dimension of the stratum of the moduli of pointed curves by Weierstrass gaps

2018/11/30 by André Contiero, Contiero, Andre, Aislan Leal Fontes +3
Mathematics · Engineering · Computer Science · #Algebraic Geometry and Number Theory #Advanced Numerical Analysis Techniques #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.1811.12894

Abstract

The dimension of the moduli space of smooth pointed curves with prescribed Weierstrass semigroup at the market point is computed for three families of symmetric semigroups of multiplicity six. We also collect the dimensions of such moduli spaces for all semigroups of genus not greater than seven. A question related to an improvement of a Deligne--Pinkham's bound is also formulated, suggesting that the positive graded part of the first module of the cotangent complex associated to a semigroup algebra is a missing invariant. The answer for this question is positive for all these moduli that we know their dimensions.

Citations

• On the locus of curves with an odd subcanonical marked point

Related

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• The Dimension of the Moduli Space of Pointed Algebraic Curves of Low Genus
• Local Complete Intersections and Weierstrass Points
• Generalized Weierstrass semigroups at several points on certain maximal curves which cannot be covered by the Hermitian curve
• Birational Geometry of moduli spaces of pointed curves