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21.
Karin Erdmann Miles Holloway Rachel Taillefer Nicole Snashall Øyvind Solberg 《K-Theory》2004,33(1):67-87
Support varieties for any finite dimensional algebra over a field were introduced in (Proc. London Math. Soc. 88 (3) (2004) 705–732) using graded subalgebras of the Hochschild cohomology ring. We mainly study these varieties for selfinjective algebras under appropriate finite generation hypotheses. Then many of the standard results from the theory of support varieties for finite groups generalize to this situation. In particular, the complexity of the module equals the dimension of its corresponding variety, all closed homogeneous varieties occur as the variety of some module, the variety of an indecomposable module is connected, the variety of periodic modules are lines and for symmetric algebras a generalization of Webbs theorem is true. As a corollary of a more general result we show that Webbs theorem generalizes to finite dimensional cocommutative Hopf algebras.Received November 2003Mathematics Subject Classifications (2000) Primary: 16E40, 16G10, 16P10, 16P20; Secondary: 16G70. 相似文献
22.
23.
We prove that the varieties
of complete pairs of zero-dimensional subschemes of lengths d
1 2, d
2 4 on a smooth irreducible projective algebraic surface are singular. 相似文献
24.
Paul Valery A. Bressler 《Compositio Mathematica》2003,135(3):245-278
We consider a fan as a ringed space (with finitely many points). We develop the corresponding sheaf theory and functors, such as direct image R* ( is a subdivision of a fan), Verdier duality, etc. The distinguished sheaf
, called the minimal sheaf plays the role of an equivariant intersection cohomology complex on the corresponding toric variety (which exists if is rational). Using
we define the intersection cohomology space IH(). It is conjectured that a strictly convex piecewise linear function on acts as a Lefschetz operator on IH(). We show that this conjecture implies Stanley's conjecture on the unimodality of the generalized h-vector of a convex polytope. 相似文献
25.
Jaya N. Iyer 《Compositio Mathematica》2003,136(3):317-321
In this paper, we show that the Chern classes c
k
of the de Rham bundle
defined on any good toroidal compactification
of the moduli space of Abelian varieties of dimension g are zero in the rational Chow ring of
, for g=4, 5 and k>0. 相似文献
26.
In (Deodhar, Geom. Dedicata, 36(1) (1990), 95–119), Deodhar proposes a combinatorial framework for determining the Kazhdan-Lusztig polynomials P
x
,
w
in the case where W is any Coxeter group. We explicitly describe the combinatorics in the case where
(the symmetric group on n letters) and the permutation w is 321-hexagon-avoiding. Our formula can be expressed in terms of a simple statistic on all subexpressions of any fixed reduced expression for w. As a consequence of our results on Kazhdan-Lusztig polynomials, we show that the Poincaré polynomial of the intersection cohomology of the Schubert variety corresponding to w is (1+q)
l(w)
if and only if w is 321-hexagon-avoiding. We also give a sufficient condition for the Schubert variety X
w
to have a small resolution. We conclude with a simple method for completely determining the singular locus of X
w
when w is 321-hexagon-avoiding. The results extend easily to those Weyl groups whose Coxeter graphs have no branch points (B
C
n
, F
4, G
2). 相似文献
27.
Anthony Bahri Martin Bendersky 《Transactions of the American Mathematical Society》2000,352(3):1191-1202
Toric manifolds, a topological generalization of smooth projective toric varieties, are determined by an -dimensional simple convex polytope and a function from the set of codimension-one faces into the primitive vectors of an integer lattice. Their cohomology was determined by Davis and Januszkiewicz in 1991 and corresponds with the theorem of Danilov-Jurkiewicz in the toric variety case. Recently it has been shown by Buchstaber and Ray that they generate the complex cobordism ring. We use the Adams spectral sequence to compute the -theory of all toric manifolds and certain singular toric varieties.
28.
Christos Tatakis Apostolos Thoma 《Journal of Combinatorial Theory, Series A》2011,118(5):1540-1548
The universal Gröbner basis of an ideal is a Gröbner basis with respect to all term orders simultaneously. We characterize in graph theoretical terms the elements of the universal Gröbner basis of the toric ideal of a graph. We also provide a new degree bound. Finally, we give examples of graphs for which the true degrees of their circuits are less than the degrees of some elements of the Graver basis. 相似文献
29.
Claudia A. Sanza 《Central European Journal of Mathematics》2008,6(3):372-383
n×m-valued Łukasiewicz algebras with negation were introduced and investigated in [20, 22, 23]. These algebras constitute a
non trivial generalization of n-valued Łukasiewicz-Moisil algebras and in what follows, we shall call them n×m-valued Łukasiewicz-Moisil algebras (or LM
n×m
-algebras). In this paper, the study of this new class of algebras is continued. More precisely, a topological duality for
these algebras is described and a characterization of LM
n×m
-congruences in terms of special subsets of the associated space is shown. Besides, it is determined which of these subsets
correspond to principal congruences. In addition, it is proved that the variety of LM
n×m
-algebras is a discriminator variety and as a consequence, certain properties of the congruences are obtained. Finally, the
number of congruences of a finite LM
n×m
-algebra is computed.
相似文献
30.
Ngaiming Mok 《中国科学A辑(英文版)》2008,51(4):660-684
In 1993,Tsal proved that a proper holomorphic mapping f:Ω→Ω' from an irreducible bounded symmetric domainΩof rank≥2 into a bounded symmetric domainΩ' is necessarily totally geodesic provided that r':=rank(Ω')≤rank(Ω):= r,proving a conjecture of the author's motivated by Hermitian metric rigidity.As a first step in the proof,Tsai showed that df preserves almost everywhere the set of tangent vectors of rank 1.Identifying bounded symmetric domains as open subsets of their compact duals by means of the Borel embedding,this means that the germ of f at a general point preserves the varieties of minimal rational tangents(VMRTs). In another completely different direction Hwang-Mok established with very few exceptions the Cartan- Fubini extension priniciple for germs of local biholomorphisms between Fano manifolds of Picard num- ber 1,showing that the germ of map extends to a global biholomorphism provided that it preserves VMRTs.We propose to isolate the problem of characterization of special holomorphic embeddings between Fano manifolds of Picard number 1,especially in the case of classical manifolds such as ratio- nal homogeneous spaces of Picard number 1,by a non-equidimensional analogue of the Cartan-Fubini extension principle.As an illustration we show along this line that standard embeddings between com- plex Grassmann manifolds of rank≤2 can be characterized by the VMRT-preserving property and a non-degeneracy condition,giving a new proof of a result of Neretin's which on the one hand paves the way for far-reaching generalizations to the context of rational homogeneous spaces and more generally Fano manifolds of Picard number 1,on the other hand should be applicable to the study of proper holomorphic mappings between bounded domains carrying some form of geometric structures. 相似文献