Spectral morphisms between Banach algebras are useful for comparing their K-theory and their “noncommutative dimensions” as expressed by various notions of stable ranks. In practice, one often encounters situations where the spectral information is only known over a dense subalgebra. We investigate such relatively spectral morphisms. We prove a relative version of the Density Theorem regarding isomorphism in K-theory. We also solve Swan's problem for the connected stable rank, in fact for an entire hierarchy of higher connected stable ranks that we introduce. 相似文献
The purpose of this paper is to define cohomology complexes and study deformation theory of Hom-associative algebra morphisms and Hom-Lie algebra morphisms. We discuss infinitesimal deformations, equivalent deformations and obstructions. Moreover, we provide various examples. 相似文献
Each smooth elliptic Calabi-Yau 4-fold determines both a three-dimensional physical theory (a compactification of “M-theory”) and a four-dimensional physical theory (using the “F-theory” construction). A key issue in both theories is the calculation of the “superpotential” of the theory, which by a result of Witten is determined by the divisors D on the 4-fold satisfying X(
D = 1. We propose a systematic approach to identify these divisors, and derive some criteria to determine whether a given divisor indeed contributes. We then apply our techniques in explicit examples, in particular, when the base B of the elliptic fibration is a toric variety or a Fano 3-fold.
When B is Fano, we show how divisors contributing to the superpotential are always “exceptional” (in some sense) for the Calabi-Yau 4-fold X. This naturally leads to certain transitions of X, i.e., birational tranformations to a singular model (where the image of D no longer contributes) as well as certain smoothings of the singular model. The singularities which occur are “canonical”, the same type of singularities of a (singular) Weierstrass model. We work out the transitions. If a smoothing exists, then the Hodge numbers change.
We speculate that divisors contributing to the superpotential are always “exceptional” (in some sense) for X, also in M-theory. In fact we show that this is a consequence of the (log)-minimal model algorithm in dimension 4, which is still conjectural in its generality, but it has been worked out in various cases, among which are toric varieties. 相似文献
LetX be a smooth irreducible projective variety over an algebraically closed fieldK andE a vector bundle onX. We prove that, if dimX ≥ 1, there exist a smooth irreducible projective varietyZ overK, a surjective separable morphismf:Z →X which is finite outside an algebraic subset of codimension ≥ 3 inX and a line bundleL onX such that the direct image ofL byf is isomorphic toE. WhenX is a curve, we show thatZ, f, L can be so chosen thatf is finite and the canonical mapH1(Z, O) →H1(X, EndE) is surjective.
Dedicated to the memory of Professor K G Ramanathan 相似文献
The periodic points of a morphism of good reduction for a smooth projective curve with good reduction over
form a discrete set. This is used to give an interpretation of the morphic height in terms of asymptotic properties of periodic points, and a morphic analogue of Jensen's formula. 相似文献
To each natural deformation quantization on a Poisson manifold M we associate a Poisson morphism from the formal neighborhood of the zero section of T*M to the formal neighborhood of the diagonal of the product M×
, where
is a copy of M with the opposite Poisson structure. We call it dequantization of the natural deformation quantization. Then we 'dequantize' Fedosov's quantization. 相似文献
We give an `elementary" proof, without mentioning sites, that any section of an atomic geometric morphism is open, and any section of a connected atomic morphism is an open surjection. Previously, these results were known only for bounded morphisms. As a by-product, we obtain a proof that any connected atomic morphism with a section is necessarily bounded. 相似文献
A pointed endofunctor (and in particular a reflector) (R, r) in a category X is direct iff for each morphism f : XY the pullback of R f against rY exists and the unique fill-in morphism u from X to the pullback is such that R u is an isomorphism. (This is close to the concept of a simple reflector introduced by Cassidy, Hébert and Kelly in 1985.) We give sufficient conditions for directness, and for directness to imply reflectivity. We also relate directness to perfect morphisms, and we give several examples and counterexamples in general topology. 相似文献