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Publication date

2022-06-21

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cc-by (c) Rosa M. Miró-Roig, 2022
Please use this identifier to cite or link to this item: https://hdl.handle.net/2445/214509

Klyachko diagram of monomial ideals

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https://doi.org/10.1007/s10468-022-10146-1

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.

Subject

Varietats tòriques, Anells commutatius, Polinomis

Subject (English)

Toric varieties, Commutative rings, Polynomials

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Articles publicats en revistes (Matemàtiques i Informàtica)

Citation

MIRÓ-ROIG, Rosa M. (Rosa Maria) and SALAT MOLTÓ, Martí. Klyachko diagram of monomial ideals. Algebras And Representation Theory. 2022. Vol. 26, num. 1497-1517. ISSN 1386-923X. [consulted: 19 of August of 2026]. Available at: https://hdl.handle.net/2445/214509

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