Duality and syzygies for semimodules over numerical semigroups

Abstract

Let $\Gamma =⟨\alpha ,\beta ⟩$ be a numerical semigroup. In this article we consider the dual ${\Delta }^{\ast }$ of a $\Gamma$-semimodule $\Delta$; in particular we deduce a formula that expresses the minimal set of generators of ${\Delta }^{\ast }$ in terms of the generators of $\Delta$. As applications we compute the minimal graded free resolution of a graded $\mathbb{F}[t^{\alpha },t^{\beta }]$-submodule of $\mathbb{F}[t]$, and we investigate the structure of the selfdual $\Gamma$-semimodules, leading to a new way of counting them.

References in corpus (1)

• Compactified Jacobians and q,t-Catalan Numbers, I