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Title: | Klyachko diagram of monomial ideals |
Author: | Miró-Roig, Rosa M. (Rosa Maria) Salat Moltó, Martí |
Keywords: | Varietats tòriques Anells commutatius Polinomis Toric varieties Commutative rings Polynomials |
Issue Date: | 21-Jun-2022 |
Publisher: | Springer Verlag |
Abstract: | 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 $I^{\text {sat }}$ of $I$ from its Klyachko diagram. We use this description to compute the first local cohomology module $H_B^1(I)$. As an application, we find a formula for the Hilbert function of $I^{\text {sat }}$, and a characterization of monomial ideals with constant Hilbert polynomial, in terms of their Klyachko diagram. |
Note: | Reproducció del document publicat a: https://doi.org/10.1007/s10468-022-10146-1 |
It is part of: | Algebras And Representation Theory, 2022, vol. 26, p. 1497-1517 |
URI: | http://hdl.handle.net/2445/214509 |
Related resource: | https://doi.org/10.1007/s10468-022-10146-1 |
ISSN: | 1386-923X |
Appears in Collections: | Articles publicats en revistes (Matemàtiques i Informàtica) |
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