Abstract
We define a class of numerical semigroups S, which we call Castelnuovo semigroups, and study the subvariety Mg,1S of Mg,1 consisting of marked smooth curves with Weierstrass semigroup S. We determine the number of irreducible components of these loci and determine their dimensions. Curves with these Weierstrass semigroups are always Castelnuovo curves, which provides the basic tool for our argument. This analysis provides examples of numerical semigroups for which Mg,1S is reducible and non-equidimensional.
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