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61.
We give a new definition of the homotopical variation operators occurring in a recent high-dimensional Zariski-van Kampen theorem, a definition which opens the way to further generalizations of theorems of this kind.
62.
Carlos A. A. Florentino 《Geometriae Dedicata》2006,121(1):167-186
We obtain an explicit characterization of the stable points of the action of on the cartesian product G
× n
by simultaneous conjugation on each factor in terms of the corresponding invariant functions. From this, a simple criterion
for the irreducibility of representations of finitely generated groups into G is derived. We also obtain analogous results for the action of on the vector space of n-tuples of 2 × 2 complex matrices. For a free group F
n
of rank n, we show how to generically reconstruct the 2
n-2 conjugacy classes of representations F
n
→ G from their values under the map considered in Magnus [Math. Zeit. 170, 91–103 (1980)], defined by certain 3n − 3 traces of words of length one and two.
相似文献
63.
Standard Embeddings of Smooth Schubert Varieties in Rational Homogeneous Manifolds of Picard Number 1
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Smooth Schubert varieties in rational homogeneous manifolds of Picard number 1 are horospherical varieties. We characterize standard embeddings of smooth Schubert varieties in rational homogeneous manifolds of Picard number 1 by means of varieties of minimal rational tangents. In particular, we mainly consider nonhomogeneous smooth Schubert varieties in symplectic Grassmannians and in the 20-dimensional F_4- homogeneous manifold associated to a short simple root. 相似文献
64.
Yiqiang Li 《Advances in Mathematics》2010,224(3):1071-1096
We geometrize quantum groups of type D in the spirit of Beilinson et al. (1990) [1]. 相似文献
65.
Let f be a weight two newform for Γ1(N) without complex multiplication. In this article we study the conductor of the absolutely simple factors B of the variety Af over certain number fields L. The strategy we follow is to compute the restriction of scalars ResL/Q(B), and then to apply Milne's formula for the conductor of the restriction of scalars. In this way we obtain an expression for the local exponents of the conductor NL(B). Under some hypothesis it is possible to give global formulas relating this conductor with N. For instance, if N is squarefree, we find that NL(B) belongs to Z and , where fL is the conductor of L. 相似文献
66.
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
67.
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
68.
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
69.
70.
S. N. Il'in 《代数通讯》2013,41(9):4021-4032