Upper Bounds for the Dimension of Moduli Spaces of Algebraic Curves with Prescribed Weierstrass Semigroups
Moduli of curves | Gorenstein Curves | Weierstrass Points | Symmetric Semigroups.
In this thesis we present an implementable method to produce upper bounds for the dimension of moduli spaces of pointed curves with prescribed symmetric Weierstrass semigroup. In certain examples the upper bounds produced are optimal, when we know the dimension of the moduli space. Moreover, we are able to handle with families of symmetric semigroups with a fixed multiplicity. Applying our method to two families of symmetric semigroups we get better bounds from those given by Deligne’s Formula and Eisenbud–Harris expected dimension.