Injective Hulls of T0 Topological Fibre Spaces

We investigate the existence of injective hulls (with respect to the class of embeddings) in the categories Top ₀/B of T₀ topological fibre spaces over B. We prove that, if f:AB has a restriction to the image injective in Top ₀/f(A), (A,f) has an injective hull in Top ₀/B if and only if f(A) is locally closed in B, where A denotes the union of non-indiscrete fibres of f.     

A Theorem of Liouville Type for p-Harmonic Morphisms

In this article we prove a Liouville type theorem for p-harmonic morphisms. We show that if : MNis a p-harmonic morphism (p2) from a complete noncompact Riemannian manifold Mof nonnegative Ricci curvature into a Riemannian manifold Nof nonpositive scalar curvature such that the p-energy E _p (), or (2p–2)-energy E _2p–2() is finite, then is constant.     

预加法范畴中态射的（1,...,i）—逆

在文[7]基础上,本文研究了预加法范畴中态射的(1,…,i)一逆,证得了这些广义逆的全套表达式,从而得到了一些特殊态射广义逆的相应结果。     

Harmonic morphisms with one-dimensional fibres on Einstein manifolds

We prove that, from an Einstein manifold of dimension greater than or equal to five, there are just two types of harmonic morphism with one-dimensional fibres. This generalizes a result of R.L. Bryant who obtained the same conclusion under the assumption that the domain has constant curvature.

     

A morphism of intersection homology induced by an algebraic map

Let be a map of algebraic varieties. Barthel, Brasselet, Fieseler, Gabber and Kaup have shown that there exists a homomorphism of intersection homology groups compatible with the induced homomorphism on cohomology. The crucial point in the argument is reduction to the finite characteristic. We give an alternative and short proof of the existence of a homomorphism . Our construction is an easy application of the Decomposition Theorem.

     

关于正则态射的广义Moore-Penrose逆

通过态射的正则性,讨论加法范畴中态射的广义Moore-Penrose逆.给出了正则态射的广义Moore-Penrose逆存在的几个充要条件以及广义Moore-Penrose逆的表达式.     

-coarse geometry of complements of Z-sets in the Hilbert cube

Motivated by the Chapman Complement Theorem, we construct an isomorphism between the topological category of compact Z-sets in the Hilbert cube and the -coarse category of their complements. The -coarse morphisms are, in this particular case, intrinsically related to uniformly continuous proper maps. Using that fact we are able to relate in a natural way some of the topological invariants of Z-sets to the geometry of their complements.

     

具有泛分解态射的加权Moore-Penrose逆

讨论了预加法范畴C中具有泛分解态射的加权Moore-Penrose逆,并给出了具有泛分解态射的加权Moore-Penrose逆存在的几个充要条件,以及具有泛分解态射的加权Moore-Penrose逆的表达式,推广了关于具有泛分解态射的广义Moore-Penrose逆的相应结果.     

On Classification of Projective Varieties with Non-Integral Nef Values

61. IntroductionLetM be an n-dimensional normal projective variety with only Q-Gorenstein, terminalsingUlarities and letL be an ample line bundle on M. KM denotes the canonical divisor, orthe canonical sheaf of M. Assume that KM is not nef. The ne f value of (M, L) is a realnUmber defined as follows:.T = min{r E RIKM rL is ne f }.By the Kawamata rationality theorem, T is a rational number and by the KawamataShokurov base point free theorem, lin(KM AL)l is base point free for m>…     

Decomposition of Log Crepant Birational Morphisms between Log Terminal Surfaces

We prove that every log crepant birational morphism between log terminal surfaces can be decomposed into log flopping type divisorial contraction morphisms and log blowdowns. Repeating these two kinds of contractions, we reach a minimal log minimal surface from any log minimal surface.