共查询到20条相似文献,搜索用时 78 毫秒
1.
Using vertex algebra techniques, we determine a set of generators for the cohomology ring of the Hilbert schemes of points
on an arbitrary smooth projective surface over the field of complex numbers.
Received: 28 November 2000 / Published online: 23 May 2002 相似文献
2.
Vlad Timofte 《Annals of Combinatorics》2005,9(4):495-499
We give a criterion for bases of the ring of symmetric functions in n indeterminates over a commutative ring R with identity. A related algorithm is presented in the last section.
Received April 13, 2004 相似文献
3.
Andrea Blunck 《Linear algebra and its applications》2010,433(3):672-680
Any set of σ-Hermitian matrices of size n×n over a field with involution σ gives rise to a projective line in the sense of ring geometry and a projective space in the sense of matrix geometry. It is shown that the two concepts are based upon the same set of points, up to some notational differences. 相似文献
4.
《Quaestiones Mathematicae》2013,36(4):241-247
Abstract A ring R is (right) strongly prime (SP) if every nonzero two sided ideal contains a finite set whose right annihilator is zero, SP rings have been studied by Handelman and Lawrence who raised the problem of characterizing SP group algebras. They showed that if R is SP and G is torsion free Abelian, then the group ring RG is SP. The aim of this note is to determine some more group rings which are SP. For a ring R we also define the strongly prime radical s(R). We then show that s(R)G = s(W) for certain classes of groups. 相似文献
5.
Dariush Kiani Mohsen Molla Haji Aghaei Borworn Suntornpoch 《Linear algebra and its applications》2011,435(6):1336-1343
This work is based on ideas of Ili? [A. Ili?, The energy of unitary Cayley graphs, Linear Algebra Appl. 431 (2009) 1881-1889] on the energy of unitary Cayley graph. For a finite commutative ring R with unity , the unitary Cayley graph of R is the Cayley graph whose vertex set is R and the edge set is {{a,b}:a,b∈Randa-b∈R×}, where R× is the group of units of R. We study the eigenvalues of the unitary Cayley graph of a finite commutative ring and some gcd-graphs and compute their energy. Moreover, we obtain the energy for the complement of unitary Cayley graphs. 相似文献
6.
Alexandra Shlapentokh 《Journal of Number Theory》2009,129(10):2227-2259
7.
Samuel Boissière 《Mathematische Zeitschrift》2006,252(3):533-555
When the quotient of a symplectic vector space by the action of a finite subgroup of symplectic automorphisms admits as a
crepant projective resolution of singularities the Hilbert scheme of regular orbits of Nakamura, then there is a natural isomorphism
between the Grothendieck group of this resolution and the representation ring of the group, given by the Bridgeland-King-Reid
map. However, this isomorphism is not compatible with the ring structures. For the Hilbert scheme of points on the affine
plane, we study the multiplicative behavior of this map. 相似文献
8.
Let R be a commutative noetherian local ring and consider the set of isomorphism classes of indecomposable totally reflexive R-modules. We prove that if this set is finite, then either it has exactly one element, represented by the rank 1 free module, or R is Gorenstein and an isolated singularity (if R is complete, then it is even a simple hypersurface singularity). The crux of our proof is to argue that if the residue field has a totally reflexive cover, then R is Gorenstein or every totally reflexive R-module is free. 相似文献
9.
A. V. Karzanov 《Combinatorica》1985,5(4):325-335
A family ℱ of cuts of an undirected graphG=(V, E) is known to have the weak MFMC-property if (i) ℱ is the set ofT-cuts for someT⊆V with |T| even, or (ii) ℱ is the set of two-commodity cuts ofG, i.e. cuts separating any two distinguished pairs of vertices ofG, or (iii) ℱ is the set of cuts induced (in a sense) by a ring of subsets of a setT⊆V. In the present work we consider a large class of families of cuts of complete graphs and prove that a family from this class
has the MFMC-property if and only if it is one of (i), (ii), (iii). 相似文献
10.
We base ourselves on the construction of the two-dimensional random interlacements (Comets et al., 2016) to define the one-dimensional version of the process. For this, we consider simple random walks conditioned on never hitting the origin. We compare this process to the conditional random walk on the ring graph. Our results are the convergence of the vacant set on the ring graph to the vacant set of one-dimensional random interlacements, a central limit theorem for the interlacements’ local time and the convergence in law of the local times of the conditional walk on the ring graph to the interlacements’ local times. 相似文献
11.
Luc Lapointe 《Advances in Mathematics》2007,213(1):183-204
We study k-Schur functions characterized by k-tableaux, proving combinatorial properties such as a k-Pieri rule and a k-conjugation. This new approach relies on developing the theory of k-tableaux, and includes the introduction of a weight-permuting involution on these tableaux that generalizes the Bender-Knuth involution. This work lays the groundwork needed to prove that the set of k-Schur Littlewood-Richardson coefficients contains the 3-point Gromov-Witten invariants; structure constants for the quantum cohomology ring. 相似文献
12.
We obtain explicit generators for the centre of the Ringel-Hall algebra of a cyclic quiver and define a canonical algebra
monomorphism from Macdonald's ring of symmetric functions to the centre, which furthermore respects the comultiplication and
the symmetric bilinear form.
Dedicated to Claus Michael Ringel on the occasion of his 60th birthday 相似文献
13.
Henning Krause 《Mathematische Annalen》1999,313(1):95-108
Let be the stable category of finitely generated modular representations of a finite group G over a field k. We prove a Krull-Remak-Schmidt theorem for thick subcategories of . It is shown that every thick tensor-ideal of (i.e. a thick subcategory which is a tensor ideal) has a (usually infinite) unique decomposition into indecomposable thick tensor-ideals. This decomposition follows from a decomposition of the corresponding idempotent
kG-module into indecomposable modules. If is the thick tensor-ideal corresponding to a closed homogeneous subvariety W of the maximal ideal spectrum of the cohomology ring , then the decomposition of reflects the decomposition of W into connected components.
Received: 27 April 1998 / In revised form: 16 July 1998 相似文献
14.
X.W.C. Faber 《Journal of Number Theory》2007,124(1):248-257
A two-dimensional Besicovitch set over a finite field is a subset of the finite plane containing a line in each direction. In this paper, we conjecture a sharp lower bound for the size of such a subset and prove some results toward this conjecture. 相似文献
15.
Greg W. Anderson 《Advances in Mathematics》2002,172(2):169-205
The abeliant is a polynomial rule which to each n×n by n+2 array with entries in a commutative ring with unit associates an n×n matrix with entries in the same ring. The theory of abeliants, first introduced in an earlier paper of the author, is simplified and extended here. Now let J be the Jacobian of a nonsingular projective algebraic curve defined over an algebraically closed field. With the aid of the theory of abeliants we obtain explicit defining equations for J and its group law. 相似文献
16.
A.A. Lopatin 《Linear algebra and its applications》2011,434(8):1920-1944
A minimal (by inclusion) generating set for the algebra of semi-invariants of a quiver of dimension (2,…,2) is established over an infinite field of arbitrary characteristic. The mentioned generating set consists of the determinants of generic matrices and the traces of tree paths of pairwise different multidegrees, where in the case of characteristic different from two we take only admissible paths. As a consequence, we describe relations modulo decomposable semi-invariants. 相似文献
17.
Iwona W?och 《Discrete Mathematics》2008,308(20):4768-4772
A subset S of vertices of a graph G is independent if no two vertices in S are adjacent. In this paper we study maximal (with respect to set inclusion) independent sets in trees including the set of leaves. In particular the smallest and the largest number of these sets among n-vertex trees are determined characterizing corresponding trees. We define a local augmentation of trees that preserves the number of maximal independent sets including the set of leaves. 相似文献
18.
In a previous paper we have announced that a graph is non-planar if and only if it contains a maximal, strict, compact, odd
ring. Little has conjectured that the compactness condition may be removed. Chernyak has now published a proof of this conjecture.
However, it is difficult to test a ring for maximality. In this paper we show that for odd rings of size five or greater,
the condition of maximality may be replaced by a new one called regularity. Regularity is an easier condition to diagnose
than is maximality. 相似文献
19.
Henning Bruhn 《Linear algebra and its applications》2011,435(8):2007-967
Motivated by work of Diestel and Kühn on the cycle spaces of infinite graphs we study the ramifications of allowing infinite sums in a module RM. We show that every generating set in this setup contains a basis if the ground set M is countable, but not necessarily otherwise. Given a family N⊆RM, we determine when the infinite-sum span N of N is closed under infinite sums, i.e. when N=N. We prove that this is the case if R is a field or a finite ring and each element of M lies in the support of only finitely many elements of N. This is, in a sense, best possible. We finally relate closures under infinite sums to topological closures in the product space RM. 相似文献
20.
Bruce Olberding 《Journal of Pure and Applied Algebra》2018,222(8):2267-2287
Let F be a field. For each nonempty subset X of the Zariski–Riemann space of valuation rings of F, let and , where denotes the maximal ideal of V. We examine connections between topological features of X and the algebraic structure of the ring . We show that if and is a completely integrally closed local ring that is not a valuation ring of F, then there is a space Y of valuation rings of F that is perfect in the patch topology such that . If any countable subset of points is removed from Y, then the resulting set remains a representation of . Additionally, if F is a countable field, the set Y can be chosen homeomorphic to the Cantor set. We apply these results to study properties of the ring with specific focus on topological conditions that guarantee is a Prüfer domain, a feature that is reflected in the Zariski–Riemann space when viewed as a locally ringed space. We also classify the rings where X has finitely many patch limit points, thus giving a topological generalization of the class of Krull domains, one that includes interesting Prüfer domains. To illustrate the latter, we show how an intersection of valuation rings arising naturally in the study of local quadratic transformations of a regular local ring can be described using these techniques. 相似文献