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pro vyhledávání: '"13h10"'
Autor:
Miyashita, Sora, Varbaro, Matteo
In this paper we prove that nearly Gorenstein Stanley-Reisner rings of dimension at least 3 are indeed Gorenstein. By previous work of the first author this yields a complete characterization of nearly Gorenstein Stanley-Reisner rings. We also show t
Externí odkaz:
http://arxiv.org/abs/2412.12860
Autor:
Hang, Nguyen Thi Anh, Nhan, Le Thanh
Let $(R, \frak m)$ be a Noetherian local ring. This paper deals with the annihilator of Artinian local cohomology modules $H^i_{\frak m}(M)$ in the relation with the structure of the base ring $R$, for non negative integers $i$ and finitely generated
Externí odkaz:
http://arxiv.org/abs/2412.06280
In this article, we deduce test properties, in the sense of finitely many vanishing of Ext or Tor, of CM (Cohen-Macaulay) modules whose multiplicity and number of generators (resp., type) are related by certain inequalities. We apply these test behav
Externí odkaz:
http://arxiv.org/abs/2412.01636
Autor:
Takahashi, Ryo
We define a uniformly dominant local ring as a commutative noetherian local ring with an integer r such that the residue field is built from any nonzero object in the singularity category by direct summands, shifts and at most r mapping cones. We fin
Externí odkaz:
http://arxiv.org/abs/2412.00669
The complexity and curvature of a module, introduced by Avramov, measure the growth of Betti and Bass numbers of a module, and distinguish the modules of infinite homological dimension. The notion of complexity was extended by Avramov-Buchweitz to pa
Externí odkaz:
http://arxiv.org/abs/2411.17622
Let $A$ be an excellent two-dimensional normal local ring containing an algebraically closed field. Then $A$ is called an elliptic singularity if $p_f(A)=1$, where $p_f$ denotes the fundamental genus. On the other hand, the concept of almost Gorenste
Externí odkaz:
http://arxiv.org/abs/2410.23911
Autor:
Buczyński, Jarosław, Keneshlou, Hanieh
The $r$-th cactus variety of a subvariety $X$ in a projective space generalizes the $r$-th secant variety of $X$ and it is defined using linear spans of finite subschemes of $X$ of degree $r$. One of its original purposes was to study the vanishing s
Externí odkaz:
http://arxiv.org/abs/2410.21908
Autor:
Ishii, Shihoko, Yoshida, Ken-ichi
We show the vanishing of the first direct image of the structure sheaf of a normal scheme $X$ which is mapped properly and birationally over a regular scheme of any dimension. On the other hand, for any dimension greater than two, we show examples of
Externí odkaz:
http://arxiv.org/abs/2410.15282
Autor:
Tavanfar, Ehsan
We show that any complete local (normal) domain admits a module-finite quasi-Gorenstein normal (complete local) domain extension. Notably our result resolves the previously open case of residual characteristic two.
Comment: Comments are very wel
Comment: Comments are very wel
Externí odkaz:
http://arxiv.org/abs/2410.15149
In this paper, we investigate problems concerning when the residue field $k$ of a local ring $(R,\frak m$, $k)$ appears as a direct summand of syzygy modules, from two perspectives. First, we prove that the following conditions are equivalent: (i) $k
Externí odkaz:
http://arxiv.org/abs/2410.12227