On generalized Weierstrass semigroups in linearized function fields

Abstract

In this article, using the notion of discrepancies, we study the generalized Weierstrass semigroup $\widehat{H}(\mathbf{Q})$, where $\mathbf{Q}$ is an $n$-tuple of distinct totally ramified places of degree one in a linearized function field. As a consequence, we characterize and explicitly determine the sets of absolute maximal elements $\widehatΓ(\mathbf{Q})$ and relative maximal elements $\widehatΛ(\mathbf{Q})$, generalizing the existing results in the literature. Finally, we apply our results to some classes of algebraic curves.