相关论文: The Structure of Ulrich ideals in hypersurfaces
The objective of this article is to give an effective algebraic characterization of normal crossing hypersurfaces in complex manifolds. It is shown that a hypersurface has normal crossings if and only if it is a free divisor, has a radical…
We give a lower bound on the Ulrich complexity of hypersurfaces of dimension $n \ge 6$. The bound improves the result in [BES] for $n \le 78$.
We classify the possible shapes of minimal free resolutions over a regular local ring. This illustrates the existence of free resolutions whose Betti numbers behave in surprisingly pathological ways. We also give an asymptotic…
This is the first in a series of papers where we develop new structural elements on singular area minimizing hypersurfaces, the skin structures. They disclose previously unapproachable and largely unexpected geometric and analytic…
For an Ulrich ideal in a Gorenstein local ring, the quotient ring is again Gorenstein. Aiming to further develop the theory of Ulrich ideals, this paper investigates a naive question of how many non-principal ideals whose quotient rings are…
In this paper we present a constructive method to characterize ideals of the local ring $\mathscr{O}_{\mathbb{C}^n,0}$ of germs of holomorphic functions at $0\in\mathbb{C}^n$ which arise as the moduli ideal $\langle f,\mathfrak{m}\,…
In this paper, we study hypersurfaces of Euclidean spaces with arbitrary dimension. First, we obtain some results on $\mbox{H}$-hypersurfaces. Then, we give the complete classification of $\mbox{H}$-hypersurfaces with 3 distinct curvatures.…
In this paper, geometric characterizations of conformally flat and radially flat hypersurfaces in $\mathbb{S}^n \times \mathbb{R}$ and $\mathbb{H}^n \times \mathbb{R}$ are given by means of their extrinsic geometry. Under suitable…
The Euler characteristic of a very affine variety encodes the number of critical points of the likelihood equation on this variety. In this paper, we study the Euler characteristic of the complement of a hypersurface arrangement with…
This article studies the notion of $S-r-$ideals in commutative ring $H$, where $S$ is a multiplicatively closed subset of $H$. Some basic properties of $S-r-$ideals are given. Various characterizations of $S-r-$ideals are presented. Also,…
The set of all maximal ideals of the ring $\mathcal{M}(X,\mathcal{A})$ of real valued measurable functions on a measurable space $(X,\mathcal{A})$ equipped with the hull-kernel topology is shown to be homeomorphic to the set $\hat{X}$ of…
A local Cohen--Macaulay ring is called Ulrich-split if any short exact sequence of Ulrich modules split. In this paper we initiate the study of Ulrich split rings. We prove several necessary or sufficient criteria for this property, linking…
The concept of hypergroup is generalization of group, first was introduced by Marty [9]. This theory had applications to several domains. Marty had applied them to groups, algebraic functions and rational functions. M. Krasner has studied…
Consideration of certain properties of group rings and their ideals search
The Tjurina ideal of a germ of an holomorphic function $f$ is the ideal of $\mathscr{O}_{\mathbbm{C}^n,0}$ - the ring of those germs at $0\in\mathbbm{C}^n$ - generated by $f$ itself and by its partial derivatives. Here it is denoted by…
After recalling the definition and basic properties of Ulrich bundles, we focus on the existence problem: does any smooth projective variety carry a Ulrich bundle? We show that the Serre construction provides a positive answer on certain…
The present paper studies structure of the ring of integer-valued entire functions. We characterize certain classes of prime and maximal ideals and investigate some of their properties.
In this note we generalize the main result in [DIV: R. Di Gennaro, G. Ilardi, J. Valles, Singular hypersurfaces characterizing the Lefschetz properties J. Lond. Math. Soc. (2) 89 (2014), no. 1, 194-212] on artinian ideals failing Lefschetz…
We search for principal ideals. As a sample, let $R$ be a strongly-normal, almost-factorial, and complete-intersection local ring with a prime ideal $P$ of height one. If $depth(R/ P)\geq dim R-2$, we show $P$ is principal. As an immediate…
We give an explicit description of cubic rings over a discrete valuation ring, as well as a description of all ideals of such rings.