Bounds on Multigraded Regularity
| Autor: | Bruce, Juliette, Heller, Lauren Cranton, Sayrafi, Mahrud |
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| Rok vydání: | 2022 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | We explore the asymptotic behavior of the multigraded Castelnuovo--Mumford regularity of powers of ideals. Specifically, if $I$ is an ideal in the total coordinate ring $S$ of a smooth projective toric variety $X$, we bound the region $\operatorname{reg}(I^n)\subset\operatorname{Pic} X$ by proving that it contains a translate of the regularity of $S$ and is contained in a translate of the nef cone of $X$. Each bound translates by a fixed vector as $n$ increases. Along the way we prove that the multigraded regularity of a finitely generated torsion-free module is contained in a translate of the nef cone determined by the degrees of the generators of $M$, and thus contains only finitely many minimal elements. Comment: 11 pages |
| Databáze: | arXiv |
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