Abstract
In this paper we study the syzygy modules of a grid or a fat grid of \({\mathbb{P}^n_{\bf K}}\). We compute the minimal free resolution for the ideal of a complete grid in \({\mathbb{P}^3_{\bf K}}\), and we conjecture this resolution in \({\mathbb{P}^n_{\bf K}}\). Moreover we compute the minimal free resolution for the ideal of an incomplete grid of \({\mathbb{P}^3_{\bf K}}\). We also conjecture the minimal free resolution for the ideal of a fat complete grid in \({\mathbb{P}^3_{\bf K}}\).
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