Duality and syzygies for semimodules over numerical semigroups

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

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