On the generalized Scarf complex of lattice ideals

Abstract

Let $k$ be a field, $\mathcal{L}\subset {\mathbb{Z}}^n$ be a lattice such that $Ł\cap {\mathbb{N}}^n=\{0\}$, and $I_{Ł}\subset \mathbb{k}[x_1,...,x_n]$ the corresponding lattice ideal. We present the generalized Scarf complex of $I_{Ł}$ and show that it is indispensable in the sense that it is contained in every minimal free resolution of $R/I_{Ł}$.

15 pages