  We provide a new lower bound for the dimension of the moduli space of smooth
pointed curves with prescribed Weierstrass semigroup at the marked point,
derived from the Deligne-Greuel formula and Pinkham's equivariant deformation
theory. Using Buchweitz's description of the first cohomology module of the
cotangent complex for monomial curves, we show that our lower bound improves a
recently one given by Pflueger. By allowing semigroups running over suitable
families of symmetric semigroups of multiplicity six, we show that this new
lower bound is attained, and that the corresponding moduli spaces are non-empty
and of pure dimension.
