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 \cite{D}, we present a description of these elements which generalizes the approach of Homma and Kim \cite{HK} 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.