Zobrazeno 1 - 10
of 63
pro vyhledávání: '"Berkesch, Christine"'
Autor:
Bailly-Hall, Isidora, Berkesch, Christine, Dovgodko, Karina, Guan, Sean, Sivakumar, Saisudharshan, Sun, Jishi
For finite sets of points in $\mathbb{P}^n \times \mathbb{P}^m$, we produce short virtual resolutions, as introduced by Berkesch--Erman--Smith. We first intersect with a sufficiently high power of one set of variables for points in $\mathbb{P}^n \tim
Externí odkaz:
http://arxiv.org/abs/2402.12495
We provide a sharp upper bound on the quotient of the rank of an A-hypergeometric system with a three-dimensional torus action by the normalized volume of A; in this case, the upper bound is two.
Comment: 9 pages
Comment: 9 pages
Externí odkaz:
http://arxiv.org/abs/2301.04569
Autor:
Berkesch, Christine, Chan, C-Y. Jean, Klein, Patricia, Matusevich, Laura Felicia, Page, Janet, Vassilev, Janet
Publikováno v:
Alg. Number Th. 17 (2023) 1959-1984
We give explicit descriptions of rings of differential operators of toric face rings in characteristic $0$. For quotients of normal affine semigroup rings by radical monomial ideals, we also identify which of their differential operators are induced
Externí odkaz:
http://arxiv.org/abs/2112.00266
Autor:
Berkesch, Christine, Chan, C-Y. Jean, Klein, Patricia, Matusevich, Laura Felicia, Page, Janet, Vassilev, Janet
Through examples, we illustrate how to compute differential operators on a quotient of an affine semigroup ring by a radical monomial ideal, when working over an algebraically closed field of characteristic 0.
Comment: 30 pages, 17 figures
Comment: 30 pages, 17 figures
Externí odkaz:
http://arxiv.org/abs/2105.04074
When studying a graded module $M$ over the Cox ring of a smooth projective toric variety $X$, there are two standard types of resolutions commonly used to glean information: free resolutions of $M$ and vector bundle resolutions of its sheafification.
Externí odkaz:
http://arxiv.org/abs/2012.14047
The rank of an $A$-hypergeometric $D$-module $M_A(\beta)$, associated with a full rank $(d\times n)$-matrix $A$ and a vector of parameters $\beta\in \mathbb{C}^d$, is known to be the normalized volume of $A$, denoted $\mathrm{vol}(A)$, when $\beta$ l
Externí odkaz:
http://arxiv.org/abs/1907.08669
Publikováno v:
Alg. Number Th. 14 (2020) 323-347
We compute the $L$-characteristic cycle of an $A$-hypergeometric system and higher Euler-Koszul homology modules of the toric ring. We also prove upper semicontinuity results about the multiplicities in these cycles and apply our results to analyze t
Externí odkaz:
http://arxiv.org/abs/1902.04339
We characterize the (regular) holonomicity of Horn systems of differential equations under a hypothesis that captures the most widely studied classical hypergeometric systems.
Comment: 7 pages. arXiv admin note: text overlap with arXiv:1308.5901
Comment: 7 pages. arXiv admin note: text overlap with arXiv:1308.5901
Externí odkaz:
http://arxiv.org/abs/1806.03355
Publikováno v:
Algebraic Geometry, 7 (2020) no. 4, 460-481
Syzygies capture intricate geometric properties of a subvariety in projective space. However, when the ambient space is a product of projective spaces or a more general smooth projective toric variety, minimal free resolutions over the Cox ring are t
Externí odkaz:
http://arxiv.org/abs/1703.07631