共查询到20条相似文献,搜索用时 15 毫秒
1.
Simon Goodwin 《Indagationes Mathematicae》2004,15(2):189-207
Let G be a reductive linear algebraic group, P a parabolic subgroup of G and Pu its unipotent radical. We consider the adjoint action of P on the Lie algebra u of Pu. Each higher term u(l) of the descending central series of u is stable under this action. For classical G all instances when P acts on u(l) with a finite number of orbits were determined in [9], [10], [3] and [4]. In this note we extend these results to groups of type F4 and E6. Moreover, when P acts on u(l) with an infinite number of orbits, we determine whether P still acts with a dense orbit. For G of type E7 and E8 we investigate only the case of a Borel subgroup.We present a complete classification of all instances when u(l) is a prehomogeneous space for a Borel subgroup B of a reductive algebraic group for any l ≥ 0. 相似文献
2.
The goal of this paper is to extend some previous results on abelian ideals of Borel subalgebras to so-called spherical ideals of
These are ideals
of
such that their G-saturation
is a spherical G-variety. We classify all maximal spherical ideals of
for all simple G.Received: 25 March 2004 相似文献
3.
Given a vector bundle E, on an irreducible projective variety X, we give a necessary and sufficient criterion for E to be a direct image of a line bundle under a surjective étale morphism. The criterion in question is the existence of a Cartan subalgebra bundle of the endomorphism bundle . As a corollary, a criterion is obtained for E to be the direct image of the structure sheaf under an étale morphism. The direct image of a parabolic line bundle under any ramified covering map has a natural parabolic structure. Given a parabolic vector bundle, we give a similar criterion for it to be the direct image of a parabolic line bundle under a ramified covering map. 相似文献
4.
We prove, as an analogy of a conjecture of Artin, that if
is a finite flat morphism between two singular reduced absolutely irreducible projective
algebraic curves defined over a finite field, then the numerator of the zeta function
of X divides that of Y
in
. Then, we give some interpretations of this result in terms of
semi-abelian varieties.
Received: 23 July 2001 相似文献
5.
Gerhard Röhrle 《manuscripta mathematica》1999,98(1):9-20
For a linear algebraic group G over an algebraically closed field k and a parabolic subgroup P of G the modality of P is defined to be the maximal number of parameters upon which a family of G-orbits on Lie P
u
depends and it is denoted by mod P, where P
u
is the unipotent radical of P. The principal aim of this note is a generalization of two basic “monotonicity” results from [19] to positive characteristic:
(1) If Θ is a semisimple automorphism of G and P is Θ-stable, then mod P
\Θ≤ mod P. (2) If G is reductive, char k is a good prime for G, and H is a closed reductive subgroup of G normalized by a maximal torus T⊂P of G, then mod (P∩H)≤ mod P.
Received: 22 April 1998 / Revised version: 3 July 1998 相似文献
6.
Raphaël Achet 《Journal of Pure and Applied Algebra》2017,221(11):2838-2860
We obtain an explicit upper bound on the torsion of the Picard group of the forms of and their regular completions. We also obtain a sufficient condition for the Picard group of the forms of to be nontrivial and we give examples of nontrivial forms of with trivial Picard groups. 相似文献
7.
8.
Evgenii L. Bashkirov 《Journal of Pure and Applied Algebra》2010,214(7):1049-1062
Let a field K be an algebraic extension of a subfield k of characteristic not 2, n an integer, a non-degenerate isotropic form in n variables over K with coefficients in k. We study subgroups of the orthogonal group On(K,Q) that contain the derived subgroup Ωn(k,Q) of the group On(k,Q). 相似文献
9.
Aleksander Czarnecki 《Journal of Pure and Applied Algebra》2019,223(3):1161-1166
We prove that every maximal ideal in the ring of k-regulous functions, , on a smooth real affine algebraic variety of dimension is not finitely generated. 相似文献
10.
G.I Lehrer 《Advances in Mathematics》2004,186(1):229-250
Let G be a finite unitary reflection group acting in a complex vector space . The discriminant varietyXG of G is defined as the space of regular orbits of G on V. Classical examples include the varieties of complex polynomials of degree n with distinct (resp. non-zero distinct) roots. The normaliser of G in GL(V) acts on XG; in this work we determine the action of on the cohomology of XG. In the classical cases this amounts to computing the cohomology of XG with certain local coefficient systems. Our methods are to compute equivariant weight polynomials by means of explicit counting of the rational points of certain varieties over finite fields, and then to exploit the weight purity of the relevant varieties. We obtain some power series identities as a byproduct. 相似文献
11.
Luke Oeding 《Journal of Pure and Applied Algebra》2011,215(6):1516-1527
We prove a set-theoretic version of the Landsberg-Weyman Conjecture on the defining equations of the tangential variety of a Segre product of projective spaces. We introduce and study the concept of exclusive rank. For the proof of this conjecture, we use a connection to the author’s previous work and re-express the tangential variety as the variety of principal minors of symmetric matrices that have exclusive rank no more than 1. We discuss applications to semiseparable matrices, tensor rank versus border rank, context-specific independence models and factor analysis models. 相似文献
12.
Dmitri I. Panyushev 《Advances in Mathematics》2004,186(2):307-316
We study Abelian ideals of a Borel subalgebra consisting of long roots. It is shown that methods of Cellini and Papi can be extended to this situation. A uniform expression for the number of long Abelian ideals is given. We also show that there is a one-to-one correspondence between the long Abelian ideals and B-stable commutative subalgebras in the little adjoint representation of the Langlands dual Lie algebra. 相似文献
13.
Tomasz Weiss 《Topology and its Applications》2008,156(1):138-141
We show that it is consistent with ZFC that there exist:
- (1)
- An unbounded (with respect to ?∗) and strongly measure zero subgroup of ZN, but without the Menger property.
- (2)
- An unbounded (with respect to ?∗) and strongly measure zero subgroup of ZN with the Menger property which does not have the Rothberger property.
14.
János Kollár 《Advances in Mathematics》2005,198(1):27-35
The subring of the Grothendieck ring of k-varieties generated by smooth conics is described, giving many zero divisors. The proof uses only elementary projective geometry. 相似文献
15.
The standard Poisson structure on the rectangular matrix variety Mm,n(C) is investigated, via the orbits of symplectic leaves under the action of the maximal torus T⊂GLm+n(C). These orbits, finite in number, are shown to be smooth irreducible locally closed subvarieties of Mm,n(C), isomorphic to intersections of dual Schubert cells in the full flag variety of GLm+n(C). Three different presentations of the T-orbits of symplectic leaves in Mm,n(C) are obtained: (a) as pullbacks of Bruhat cells in GLm+n(C) under a particular map; (b) in terms of rank conditions on rectangular submatrices; and (c) as matrix products of sets similar to double Bruhat cells in GLm(C) and GLn(C). In presentation (a), the orbits of leaves are parametrized by a subset of the Weyl group Sm+n, such that inclusions of Zariski closures correspond to the Bruhat order. Presentation (b) allows explicit calculations of orbits. From presentation (c) it follows that, up to Zariski closure, each orbit of leaves is a matrix product of one orbit with a fixed column-echelon form and one with a fixed row-echelon form. Finally, decompositions of generalized double Bruhat cells in Mm,n(C) (with respect to pairs of partial permutation matrices) into unions of T-orbits of symplectic leaves are obtained. 相似文献
16.
We prove that the invariant Hilbert scheme parameterising the equivariant deformations of the affine multicone over a flag variety is, under certain hypotheses, an affine space. More specifically, we obtain that the isomorphism classes of equivariant deformations of such a multicone are in correspondence with the orbits of a well-determined wonderful variety. 相似文献
17.
Recent work of Ein–Lazarsfeld–Smith and Hochster–Huneke raised the containment problem of determining which symbolic powers of an ideal are contained in a given ordinary power of the ideal. Bocci–Harbourne defined a quantity called the resurgence to address this problem for homogeneous ideals in polynomial rings, with a focus on zero-dimensional subschemes of projective space. Here we take the first steps toward extending this work to higher dimensional subschemes. We introduce new asymptotic versions of the resurgence and obtain upper and lower bounds on them for ideals I of smooth subschemes, generalizing what is done in Bocci and Harbourne (2010) [5]. We apply these bounds to ideals of unions of general lines in PN. We also pose a Nagata type conjecture for symbolic powers of ideals of lines in P3. 相似文献
18.
Given an infinitesimal group G over an algebraically closed field k of characteristic p?3, we provide criteria for the principal block B0(G) of its algebra of distributions to be of tame representation type. These are employed in conjunction with Galois coverings to determine the structure of G modulo its multiplicative center as well as the quiver and the relations of the algebra B0(G). 相似文献
19.
Kanetomo Sato 《Mathematische Zeitschrift》2007,257(4):707-743
In this paper, we define two kinds (homological and cohomological) of étale logarithmic Hodge–Witt sheaves on normal crossing
varieties over a perfect field of positive characteristic, and discuss some fundamental properties, in particular puity and
duality. 相似文献
20.
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