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Klyachko diagram of monomial ideals

Miró-Roig, Rosa M. (Rosa Maria) ; Salat Moltó, Martí

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Title:
Klyachko diagram of monomial ideals
Author: Miró-Roig, Rosa M. (Rosa Maria) ; Salat Moltó, Martí
Subjects: Anells commutatius ; Commutative rings ; Polinomis ; Polynomials ; Toric varieties ; Varietats tòriques
Notes: https://doi.org/10.1007/s10468-022-10146-1
Reproducció del document publicat a: https://doi.org/10.1007/s10468-022-10146-1
723173
1386-923X
http://hdl.handle.net/2445/214509
Algebras And Representation Theory, 2022, vol. 26, p. 1497-1517
Articles publicats en revistes (Matemàtiques i Informàtica)
Description: 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.
Publisher: Springer Verlag
Creation Date: 2022-06
Language: English

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