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61.
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
62.
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
63.
Armen Edigarian Jan Wiegerinck 《Proceedings of the American Mathematical Society》2003,131(8):2459-2465
Let be domains in . Under very mild conditions on we show that there exist holomorphic functions , defined on with the property that is nowhere extendible across , while the graph of over is not complete pluripolar in . This refutes a conjecture of Levenberg, Martin and Poletsky (1992).
64.
A -frame is a lattice in which countable joins exist and binary meets distribute over countable joins. In this paper, the category MFrm, of metric -frames, is introduced, and it is shown to be equivalent to the category MLFrm
u, of metric Lindelöf frames.Finally, it is shown that the complete metric -frames are exactly the cozero parts of complete metric Lindelöf frames. 相似文献
65.
Parallel to the study of finite-dimensional Banach spaces, there is a growing interest in the corresponding local theory of operator spaces. We define a family of Hilbertian operator spaces , , generalizing the row and column Hilbert spaces and , and we show that an atomic subspace that is the range of a contractive projection on is isometrically completely contractive to an -sum of the and Cartan factors of types 1 to 4. In particular, for finite-dimensional , this answers a question posed by Oikhberg and Rosenthal. Explicit in the proof is a classification up to complete isometry of atomic w-closed -triples without an infinite-dimensional rank 1 w-closed ideal.
66.
We study the syzygies of a codimension two ideal . Our main result is that the module of syzygies vanishing (scheme-theoretically) at the zero locus is generated by the Koszul syzygies iff is a local complete intersection. The proof uses a characterization of complete intersections due to Herzog. When is saturated, we relate our theorem to results of Weyman and Simis and Vasconcelos. We conclude with an example of how our theorem fails for four generated local complete intersections in and we discuss generalizations to higher dimensions.
67.
Let R be a homogeneous ring over an infinite field, IR a homogeneous ideal, and
I an ideal generated by s forms of degrees d
1,...,d
s
so that codim(
:I)s. We give broad conditions for when the Hilbert function of R/
or of R/(
:I) is determined by I and the degrees d
1,...,d
s
. These conditions are expressed in terms of residual intersections of I, culminating in the notion of residually S
2 ideals. We prove that the residually S
2 property is implied by the vanishing of certain Ext modules and deduce that generic projections tend to produce ideals with this property. 相似文献
68.
A 'chaos expansion' of the intersection local time functional of two independent Brownian motions in R
d
is given. The expansion is in terms of normal products of white noise (corresponding to multiple Wiener integrals). As a consequence of the local structure of the normal products, the kernel functions in the expansion are explicitly given and exhibit clearly the dimension dependent singularities of the local time functional. Their L
p
-properties are discussed. An important tool for deriving the chaos expansion is a computation of the 'S-transform' of the corresponding regularized intersection local times and a control about their singular limit. 相似文献
69.
Peter Scott Gadde A. Swarup 《Transactions of the American Mathematical Society》2001,353(12):4973-5001
We introduce the notion of a `canonical' splitting over or for a finitely generated group . We show that when happens to be the fundamental group of an orientable Haken manifold with incompressible boundary, then the decomposition of the group naturally obtained from canonical splittings is closely related to the one given by the standard JSJ-decomposition of . This leads to a new proof of Johannson's Deformation Theorem.
70.
In this work we compute the thermodynamic properties of the 3-satisfiability problem in the infinite connectivity limit. In this limit the computation can be strongly simplified and the thermodynamic properties can be obtained with a high accuracy. We find evidence for a continuous replica symmetry breaking in the region of high number of clauses, >c. 相似文献