Zobrazeno 1 - 10
of 16
pro vyhledávání: '"13D02, 14M25"'
Autor:
Banks, Maya, Brown, Michael K., Gomes, Tara, Sridhar, Prashanth, Davila, Eduardo Torres, Zotine, Alexandre
We give an overview of a Macaulay2 package for computing with the multigraded BGG correspondence. This software builds on the package BGG due to Abo-Decker-Eisenbud-Schreyer-Smith-Stillman, which concerns the standard graded BGG correspondence. In ad
Externí odkaz:
http://arxiv.org/abs/2402.12293
Autor:
Brown, Michael K., Erman, Daniel
A foundational principle in the study of modules over standard graded polynomial rings is that geometric positivity conditions imply vanishing of Betti numbers. The main goal of this paper is to determine the extent to which this principle extends to
Externí odkaz:
http://arxiv.org/abs/2302.07403
Autor:
Cobb, John
Publikováno v:
Mathematische Zeitschrift, 306 (2024) no. 27
Motivated by toric geometry, we lift machinery for understanding syzygies of curves in projective space to the setting of products of projective spaces. Using this machinery, we show an analogue of an influential result of Gruson, Peskine, and Lazars
Externí odkaz:
http://arxiv.org/abs/2301.05979
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., Erman, Daniel
We develop a notion of linear strands for multigraded free resolutions, and we prove a multigraded generalization of Green's Linear Syzygy Theorem.
Comment: Minor edits. To appear in Mathematische Annalen
Comment: Minor edits. To appear in Mathematische Annalen
Externí odkaz:
http://arxiv.org/abs/2202.00402
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
The minimal free resolution of the coordinate ring of a complete intersection in projective space is a Koszul complex on a regular sequence. In the product of projective spaces $\mathbb{P}^1 \times \mathbb{P}^1$, we investigate which sets of points h
Externí odkaz:
http://arxiv.org/abs/1905.09991
Autor:
Tchernev, Alexandre, Varisco, Marco
We introduce the notion of Betti category for graded modules over suitably graded polynomial rings, and more generally for modules over certain small categories. Our categorical approach allows us to treat simultaneously many important cases, such as
Externí odkaz:
http://arxiv.org/abs/1605.09748
This work generalizes the short resolution given in Proc. Amer. Math. Soc. \textbf{131}, 4, (2003), 1081--1091, to any affine semigroup. Moreover, a characterization of Ap\'{e}ry sets is given. This characterization lets compute Ap\'{e}ry sets of aff
Externí odkaz:
http://arxiv.org/abs/1512.00345
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