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pro vyhledávání: '"Sayrafi, Mahrud"'
Autor:
Mallory, Devlin, Sayrafi, Mahrud
The problems of finding isomorphism classes of indecomposable modules with certain properties, or determining the indecomposable summands of a module, are ubiquitous in commutative algebra, group theory, representation theory, and other fields. The p
Externí odkaz:
http://arxiv.org/abs/2412.19799
Autor:
Sayrafi, Mahrud
We prove a Horrocks-type splitting criterion for arbitrary smooth projective toric varieties under an additional hypothesis similar to the case of products of projective spaces by Eisenbud--Erman--Schreyer.
Comment: 5 pages
Comment: 5 pages
Externí odkaz:
http://arxiv.org/abs/2412.19793
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{
Externí odkaz:
http://arxiv.org/abs/2208.11115
Autor:
Brown, Michael K., Sayrafi, Mahrud
Publikováno v:
Alg. Number Th. 18 (2024) 1923-1943
Given a smooth projective toric variety $X$ of Picard rank 2, we resolve the diagonal sheaf on $X \times X$ by a linear complex of length $\dim{X}$ consisting of finite direct sums of line bundles. As applications, we prove a new case of a conjecture
Externí odkaz:
http://arxiv.org/abs/2208.00562
We explore the relationship between multigraded Castelnuovo--Mumford regularity, truncations, Betti numbers, and virtual resolutions on a product of projective spaces $X$. After proving a uniqueness theorem for certain minimal virtual resolutions, we
Externí odkaz:
http://arxiv.org/abs/2110.10705
Publikováno v:
J. Softw. Alg. Geom. 10 (2020) 51-60
We introduce the VirtualResolution package for the computer algebra system Macaulay2. This package has tools to construct, display, and study virtual resolutions for products of projective spaces. The package also has tools for generating curves in $
Externí odkaz:
http://arxiv.org/abs/1905.07022
Autor:
Sayrafi, Mahrud
Local rings are ubiquitous in algebraic geometry. Not only are they naturally meaningful in a geometric sense, but also they are extremely useful as many problems can be attacked by first reducing to the local case and taking advantage of their nice
Externí odkaz:
http://arxiv.org/abs/1710.09830
Recent work has shown that use of quantum feedback can significantly enhance both the speed and success rate of measurement-based remote entanglement generation, but it is generally unknown what feedback protocols are optimal for these tasks. Here we
Externí odkaz:
http://arxiv.org/abs/1704.00332
We explore the relationship between multigraded Castelnuovo-Mumford regularity, truncations, Betti numbers, and virtual resolutions. We prove that on a product of projective spaces $X$, the multigraded regularity region of a module $M$ is determined
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::2c0e8d270f685169cf5e7b97da5f9c08
http://arxiv.org/abs/2110.10705
http://arxiv.org/abs/2110.10705
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