Klyachko diagram of monomial ideals
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 g...
| Autores: | , |
|---|---|
| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2022 |
| País: | España |
| Institución: | Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya) |
| Repositorio: | Recercat. Dipósit de la Recerca de Catalunya |
| OAI Identifier: | oai:recercat.cat:2445/214509 |
| Acceso en línea: | https://hdl.handle.net/2445/214509 |
| Access Level: | acceso abierto |
| Palabra clave: | Varietats tòriques Anells commutatius Polinomis Toric varieties Commutative rings Polynomials |
| Sumario: | 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. |
|---|