Weierstrass semigroups on Castelnuovo curves
Nathan Pflueger

TL;DR
This paper introduces Castelnuovo semigroups, studies the associated loci of marked curves with these semigroups, and analyzes their irreducibility and dimension, revealing complex geometric structures.
Contribution
It defines Castelnuovo semigroups and characterizes the geometric properties of the loci of curves with these semigroups in moduli space.
Findings
Number of irreducible components determined
Dimensions of loci computed
Examples of reducible and non-equidimensional loci provided
Abstract
We define a class of numerical semigroups S, which we call Castelnuovo semigroups, and study the subvariety of consisting of marked smooth curves with Weierstrass semigroup S. We determine the number of irreducible components of these loci and determine their dimensions. Curves with these Weierstrass semigroups are always Castelnuovo curves, which provides the basic tool for our argument. This analysis provides examples of numerical semigroups for which is reducible and non-equidimensional.
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