On Deligne-Pinkham's bound - Jhon Ever Quispe Vargas (2019)
This Thesis is devoted to the study of the dimensions of the strata of the moduli of smooth pointed curves by xing Weierstrass semigroups at the marked point. We provide a new lower bound for the dimension of each stratum by diminishing Deligne{Pinkham's bound by the dimension of the positive graded part of the rst module of the cotangent complex associated to a suitable monomial curve. This new lower bound is better than a lower bound given recently by N. P ueger. We also prove a conditional result which provides the exact dimension when the Weierstrass semigroup is symmetric