On Weierstrass Gaps at Several Points

We consider the problem of determining Weierstrass gaps and pure Weierstrass gaps at several points. Using the notion of relative maximality in generalized Weierstrass semigroups due to Delgado (Proc Am Math Soc 108(3):627-631, 1990), we present a description of these elements which generalizes the approach of Homma and Kim (J Pure Appl Algebra 162(2-3):273-290, 2001) given for pairs. Through this description, we study the gaps and pure gaps at several points on a certain family of curves with separated variables.