Klyachko diagrams of monomial ideals
| Autor: | Miró-Roig, Rosa M., Salat-Moltó, Martí |
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| Rok vydání: | 2022 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1007/s10468-022-10146-1 |
| Popis: | In this paper, we introduce the notion of a Klyachko diagram for a monomial ideal $I$ in a certain multi-graded polynomial ring, namely the Cox ring $R$ of a smooth complete toric variety, with irrelevant maximal ideal $B$. We present procedures to compute the Klyachko diagram of $I$ from its monomial generators, and to retrieve the $B-$saturation $I^{\mathrm{sat}}$ of $I$ from its Klyachko diagram. We use this description to compute the first local cohomology module $H^{1}_{B}(I)$. As an application, we find a formula for the Hilbert function of $I^{\mathrm{sat}}$, and a characterization of monomial ideals with constant Hilbert polynomial, in terms of their Klyachko diagram. Comment: To appear in Algebras and Representation Theory |
| Databáze: | arXiv |
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