Zobrazeno 1 - 10
of 780
pro vyhledávání: '"13a02"'
Autor:
Castañeda, Ángel Luis Muñoz
We investigate the geometric foundations of the space of geometric Goppa codes using the Tsfasman-Vladut H-construction. These codes are constructed from level structures, which extend the classical Goppa framework by incorporating invertible sheaves
Externí odkaz:
http://arxiv.org/abs/2411.19088
Autor:
Boix, Alberto F., Zarzuela, Santiago
The main goal of this paper is to obtain upper bounds for the regularity of graded deficiency modules in the spirit of the one obtained by Kumini--Murai in the monomial case building upon the spectral sequence formalism developed by \`Alvarez Montane
Externí odkaz:
http://arxiv.org/abs/2412.00092
Autor:
Grimpen, Fritz, Stefanou, Anastasios
Flat-injective presentations were introduced by Miller (2020) to provide combinatorial descriptions of $\mathbb Z^n$-graded modules. We consider them in the setting of local graded rings $R$, with grading over an abelian group, and give a criterion f
Externí odkaz:
http://arxiv.org/abs/2410.17667
Autor:
Li, Haonan, Wu, Quanshui
In this note we first study regular $\mathbb{Z}$-graded local rings. We characterize commutative noetherian regular $\mathbb{Z}$-graded local rings in similar ways as in the usual local case. The characterization by the length of (homogeneous) regula
Externí odkaz:
http://arxiv.org/abs/2410.05667
Autor:
Lu, Dancheng
We extend the chain algebra, originally defined in \cite{GN} for finite distributive lattices to that of finite pure posets. We show this algebra corresponds to the Ehrhart ring of a (0,1)-polytope, termed the chain polytope, and characterize the ind
Externí odkaz:
http://arxiv.org/abs/2410.05024
Autor:
Lax, Ernesto
We introduce the Macaulay2 package SCMAlgebras. It provides functions for computing the modules of deficiency and the filter ideals, in order to check whether a module or an ideal is sequentially Cohen-Macaulay. After the basic algebraic notions and
Externí odkaz:
http://arxiv.org/abs/2409.15134
Autor:
Murray, Taylor
Let $R$ be a standard graded, finitely generated algebra over a field, and let $M$ be a graded module over $R$ with all Bass numbers finite. Set $(-)^{(n)}$ to be the $n$-th Veronese functor. We compute the Bass numbers of $M^{(n)}$ over the ring $R^
Externí odkaz:
http://arxiv.org/abs/2407.17656
Autor:
Miyashita, Sora
The nearly Gorenstein property is a generalization of the Gorenstein property. In this paper, we introduce a new property $(\natural)$ that extends the nearly Gorenstein property in semi-standard graded rings. We show $(\natural)$ relates to a proper
Externí odkaz:
http://arxiv.org/abs/2407.05629
We resolve Stillman's conjecture for families of polynomial rings that are graded by any abelian group under mild conditions. Conversely, we show that these conditions are necessary for the existence of a Stillman bound. This has applications even fo
Externí odkaz:
http://arxiv.org/abs/2406.09593
Autor:
Roshan-Zamir, Shahriyar
Over an algebraically closed field, the $\textit{double point interpolation}$ problem asks for the vector space dimension of the projective hypersurfaces of degree $d$ singular at a given set of points. After being open for 90 years, a series of pape
Externí odkaz:
http://arxiv.org/abs/2406.08602