Weierstrass semigroups on Castelnuovo curves

[摘要] We define a class of numerical semigroups S, which we call Castelnuovo semigroups, and study the subvariety M-g,1(S) of M-g,M-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 M-g,1(S) is reducible and non-equidimensional. (C) 2021 Elsevier Inc. All rights reserved.

[发布日期] 2021-09-15

[关键词] Weierstrass semigroups;Algebraic curves;Numerical semigroups;Castelnuovo curves