ag.algebraic geometry - On the dimension of moduli space of pointed curves with fixed Weierstrass semigroup

If the complement of the semigroup (the gaps) is $a_1,ldots,a_g$, then the weight is $w=sum (a_i-i)$. I think you expect codimension $w-1$ (for small $w>0$) for the space of curves of genus $g$ having the given semigroup. However, this cannot work for large $w$. Have a look at the papers of Steven Diaz.