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61.
We construct a class of projective rational varieties X of any dimension m ≥ 1, which are smooth except at a point O, with the projective space ? m as normalization, having smooth branches, and reduced projectivized tangent cone in O. The Hilbert function of X is considered and is explicitly computed when the point O is seminormal. Indeed, we study seminormality, obtaining necessary and sufficient conditions for O to be seminormal and show that in such case the tangent cone is reduced and seminormal. 相似文献
62.
V. M. Petrogradsky 《代数通讯》2013,41(3):918-928
We study Lie nilpotent varieties of associative algebras. We explicitly compute the codimension growth for the variety of strong Lie nilpotent associative algebras. The codimension growth is polynomial and found in terms of Stirling numbers of the first kind. To achieve the result we take the free Lie algebra of countable rank L(X), consider its filtration by the lower central series and shift it. Next we apply generating functions of special type to the induced filtration of the universal enveloping algebra U(L(X)) = A(X). 相似文献
63.
Giulio Cotignoli 《代数通讯》2013,41(7):2564-2573
In the mid 1970s, Hartshorne conjectured that, for all n > 7, any rank 2 vector bundles on ? n is a direct sum of line bundles. This conjecture remains still open. In this paper, we construct indecomposable rank two vector bundles on a large class of Fano toric varieties. Unfortunately, this class does not contain ? n . 相似文献
64.
65.
S. N. Il'in 《代数通讯》2013,41(9):4021-4032
66.
67.
《代数通讯》2013,41(8):3735-3752
Abstract In this paper we give an explicit formula for the Riemann-Roch map for singular schemes which are quotients of smooth schemes by diagonalizable groups. As an application we obtain a simple proof of a formula for the Todd class of a simplicial toric variety. An equivariant version of this formula was previously obtained for complete simplicial toric varieties by Brion and Vergne (Brion M. and Vergne M. ([1997]). An equivariant Riemann-Roch theorem for complete simplicial toric varieties. J. Reine. Agnew. Math.482:67–92) using different techniques. 相似文献
68.
《代数通讯》2013,41(7):3111-3133
Abstract Following Contou-Carrère (Contou-Carrère,C. (1983). Géométrie des Groupes Semi-Simples,Résolutions équivariantes et Lieu Singulier de Leurs Variétés de Schubert. Thèse d’état,Université Montpellier II (published partly as,Le Lieu singulier des variétés de Schubert (1988). Adv. Math.,71:186–221)),we consider the Bott-Samelson resolution of a Schubert variety as a variety of galleries in the Tits building associated to the situation. Using Carrell and Peterson's characterization (Carrell,J. B. (1994). The Bruhat graph of a Coxeter group,a conjecture of Deodhar,and rational smoothness of Schubert varieties. Proc. Symp. in Pure Math. 56(Part I):53–61),we prove that rational smoothness of a Schubert variety can be expressed in terms of a subspace of the Zariski tangent space called,the combinatorial tangent space. 相似文献
69.
《代数通讯》2013,41(10):3825-3842
Abstract In any finitely complete category, there is an internal notion of normal monomorphism. We give elementary conditions guaranteeing that a normal section s: Y → X of an arrow f: X → Y produces a direct product decomposition of the form X ? Y × W. We then show how these conditions gradually vanish in various algebraic contexts, such as Maltsev, protomodular and additive categories. 相似文献
70.
M.H. Lim 《Linear and Multilinear Algebra》2013,61(3):231-234
In this note we give a simple proof and an extension of a dimension inequality of Howard concerning the range of a multilinear function with vector space range by using some results on algebraic varieties. 相似文献