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41.
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
42.
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
43.
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
44.
We obtain Chern-Osserman's inequality of a complete properly immersed minimal surface in hyperbolic -space, provided the -norm of the second fundamental form of the surface is finite.
45.
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.
46.
T.K. Subrahmonian Moothathu 《Journal of Mathematical Analysis and Applications》2011,379(2):656-663
For continuous self-maps of compact metric spaces, we study the syndetically proximal relation, and in particular we identify certain sufficient conditions for the syndetically proximal cell of each point to be small. We show that any interval map f with positive topological entropy has a syndetically scrambled Cantor set, and an uncountable syndetically scrambled set invariant under some power of f. In the process of proving this, we improve a classical result about interval maps and establish that if f is an interval map with positive topological entropy and m?2, then there is n∈N such that the one-sided full shift on m symbols is topologically conjugate to a subsystem of fn2 (the classical result gives only semi-conjugacy). 相似文献
47.
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
48.
We consider a deteriorating system submitted to external and internal failures, whose deterioration level is known by means of inspections. There are two types of repairs: minimal and perfect, depending on the deterioration level, each one following a different phase-type distribution. The failures and the inspections follow different Markovian arrival processes (MAP). Under these assumptions, the system is governed by a generalized Markov process, whose state space and generator are constructed. This general model includes the phase-type renewal process as a special case. The distribution of the number of minimal and perfect repairs between two inspections are determined. A numerical application optimizing costs is performed, and different particular cases of the model are compared. 相似文献
49.
The second part of this paper deals with the systolic implementation of the computational kernel for factorial data analysis, defined in Part I, on special-purpose hardware. The framework of the study is that a sequence of different algorithms has to be performed on a unique hardware array. This fact has led us to the design of the programmable systolic array SARDA: this is a triangular array which consists of programmable nodes with local memory and programmable orthogonal connections. 相似文献
50.