We give an upper bound for the codimension in of the variety of marked curves with a given Weierstrass semigroup. The bound is a combinatorial quantity which we call the effective weight of the semigroup; it is a refinement of the weight of the semigroup, and differs from the weight precisely when the semigroup is not primitive. We prove that whenever the effective weight is less than , the variety is nonempty and has a component of the predicted codimension. These results extend previous results of Eisenbud, Harris, and Komeda to the case of nonprimitive semigroups. We also survey other cases where the codimension of is known, as evidence that the effective weight estimate is correct in wider circumstances.
"On nonprimitive Weierstrass points." Algebra Number Theory 12 (8) 1923 - 1947, 2018. https://doi.org/10.2140/ant.2018.12.1923