共查询到20条相似文献,搜索用时 15 毫秒
1.
An SI-sequence is a finite sequence of positive integers which is symmetric, unimodal and satisfies a certain growth condition. These are known to correspond precisely to the possible Hilbert functions of graded Artinian Gorenstein algebras with the weak Lefschetz property, a property shared by a nonempty open set of the family of all graded Artinian Gorenstein algebras having a fixed Hilbert function that is an SI sequence. Starting with an arbitrary SI-sequence, we construct a reduced, arithmetically Gorenstein configuration G of linear varieties of arbitrary dimension whose Artinian reduction has the given SI-sequence as Hilbert function and has the weak Lefschetz property. Furthermore, we show that G has maximal graded Betti numbers among all arithmetically Gorenstein subschemes of projective space whose Artinian reduction has the weak Lefschetz property and the given Hilbert function. As an application we show that over a field of characteristic zero every set of simplicial polytopes with fixed h-vector contains a polytope with maximal graded Betti numbers. 相似文献
2.
Reza Sazeedeh 《Journal of Pure and Applied Algebra》2007,211(3):773-783
Let R be a commutative Noetherian ring of Krull dimension d, and let a be an ideal of R. In this paper, we will study the strong cotorsioness and the Gorenstein injectivity of the section functor Γa(−) in local cohomology. As applications, we will find new characterizations for Gorenstein and regular local rings. We also study the effect of the section functors Γa(−) and the functors on the Auslander and Bass classes. 相似文献
3.
Charles N. Delzell 《Journal of Pure and Applied Algebra》2008,212(12):2612-2622
Pólya proved that if a form (homogeneous polynomial) with real coefficients is positive on the nonnegative orthant (except at the origin), then it is the quotient of two real forms with no negative coefficients. While Pólya’s theorem extends, easily, from ordinary real forms to “generalized” real forms with arbitrary rational exponents, we show that it does not extend to generalized real forms with arbitrary real (possibly irrational) exponents. 相似文献
4.
In this paper, from an arbitrary smooth projective curve of genus at least two, we construct a non-Gorenstein Cohen-Macaulay
normal domain and a nonfree totally reflexive module over it.
Received: 2 May 2006 相似文献
5.
We notice that the Maroni invariant of a trigonal Gorenstein curve of arithmetic genus g larger than four may be equal to zero, and we show that this happens if and only if the g31 admits a non-removable base point, which is necessarily a singularity of the curve. We realize and study trigonal curves on rational scrolls, which in the case, where the g31 admits a base point Q, degenerate to a cone with vertex Q. 相似文献
6.
7.
For an ideal generated by all square-free monomials of degree m in a polynomial ring R with n variables, we obtain a specific embedding of a canonical module of to itself. The construction of this explicit embedding depends on a minimal free R-resolution of an ideal generated by . Using this embedding, we give a resolution of connected sums of several copies of certain Artin -algebras where is a field. 相似文献
8.
Letterio Gatto 《Geometriae Dedicata》1995,54(3):267-300
After some foundational material concerning the so-calledWronskian k-forms, the fundamental notion ofweight sequence at a pointP of a Gorenstein curve (singular or not) is introduced. Thanks to this definition it is possible to extend the notion ofWeierstraß gaps sequence (WGS) at a singular point of a Gorenstein curve. The latter reduces to the classical one for points of smooth curves. In Sections 6 and 7, some geometrical interpretations and discussions of previous results of Widland and Lax are given, showing the naturality of the definition of WGS at a singular point.Work partially supported by GNSAGA-CNR and MURST. 相似文献
9.
Kei Nakazato 《Journal of Pure and Applied Algebra》2018,222(12):4151-4160
Elkik established a remarkable theorem that can be applied for any noetherian henselian ring. For algebraic equations with a formal solution (restricted by some smoothness assumption), this theorem provides a solution adically close to the formal one in the base ring. In this paper, we show that the theorem would fail for some non-noetherian henselian rings. These rings do not satisfy several conditions weaker than noetherianness, such as weak proregularity (due to Grothendieck et al.) of the defining ideal. We describe the resulting pathologies. 相似文献
10.
Jean Vallès 《Expositiones Mathematicae》2012,30(4):399-405
There are few different proofs of the celebrated Poncelet closure theorem about polygons simultaneously inscribed in a smooth conic and circumscribed around another. We propose a new proof, based on the link between Schwarzenberger bundles and Poncelet curves. 相似文献
11.
We find a sufficient condition that is not level based on a reduction number. In particular, we prove that a graded Artinian algebra of codimension 3 with Hilbert function cannot be level if hd≤2d+3, and that there exists a level O-sequence of codimension 3 of type for hd≥2d+k for k≥4. Furthermore, we show that is not level if , and also prove that any codimension 3 Artinian graded algebra A=R/I cannot be level if . In this case, the Hilbert function of A does not have to satisfy the condition hd−1>hd=hd+1.Moreover, we show that every codimension n graded Artinian level algebra having the Weak-Lefschetz Property has a strictly unimodal Hilbert function having a growth condition on (hd−1−hd)≤(n−1)(hd−hd+1) for every d>θ where
h0<h1<<hα==hθ>>hs−1>hs.