基于M-模糊化P-闭集族刻画M-模糊化拟阵

在已有M-模糊化拟阵的研究基础上,引入了M-模糊化秩函数及M-模糊化P-闭包算子的定义,研究了M-模糊化P-闭包算子的性质,并定义了M-模糊化P-闭集族及研究了它的基本性质,同时借助于M-模糊化拟阵的层拟阵结构,得到M-模糊化拟阵可由M-模糊化P-闭集族等价刻画这一结论.     

M-矩阵的性质与Hadamard-Fisher不等式的注记

主要研究了两个M-矩阵的比较性质与不等式,给出了M-矩阵与逆M-矩阵Hadamard-Fisher不等式等式成立的矩阵结构.     

M-模糊化P-基集族和M-模糊化P-圈集族

引入了M-模糊化p-基集族和M-模糊化p-圈集族,并研究了他们的性质.借助于层拟阵结构,得到M-模糊化拟阵可分别由M-模糊化p-基集族和M-模糊化p-圈集族等价刻画这一合理结论.     

非奇异M-矩阵的逆矩阵和M-矩阵的Hadamard积的最小特征值下界估计

给出非奇异M-矩阵的逆矩阵和M-矩阵的Hadamard积的最小特征值下界新的估计式,这些估计式都只依赖于矩阵的元素.数值例子表明,新估计式在一定条件下改进了Fiedler和Markham的猜想,也改进了其它已有的结果.     

M-矩阵Fan积最小特征值的不等式

给出两个非奇异M-矩阵A和B的Fan积最小特征值下界的新估计式,这些估计式只依赖于两个非奇异M-矩阵的元素,易于计算.数值例子表明,新估计式在一定条件下改进了其他已有的结果.     

M-模糊化拟阵的差导算子北大核心

引入M-模糊化差导算子的新概念,给出它的一些等价刻画,探讨M-模糊化拟阵、M-模糊化差导算子以及M-模糊化闭包算子之间的关系。     

M-矩阵Hadamard积的最小特征值下界的新估计式

设B和A是非奇异M-矩阵,给出B和A-1的Hadamard积的最小特征值下界τ（B°A-1）的一个新估计式,理论证明和算例表明,本文所得新估计式改进了现有的一些结果．     

Lipschitz-α算子的M-谱理论

本文运用一个选定的可逆Lip-α算子M作为尺度算子(称为谱尺度),引入两个Banach空间之间的非线性Lip-α算子的M-豫解集、M-谱集、M-谱半径、豫解集、谱集及谱半径,证明了它们的一列系重要性质,给出了M-谱的一个摄动定理,初步建立了Lip-α算子的M-谱理论,使得现有的谱理论成为其特例.     

一类Morita Contexts的M-投射左总体维数

我们引进了模的M-投射维数和环的M-左总体维数的概念,采用比较新颖简便的方法,得到了一类Morita Contexts T=R ReeR eRe,e∈R,e2=e和环的M-左总体维数之间的相等关系.     

严格对角占优M-矩阵的逆矩阵的无穷大范数的新上界

给出了严格对角占优M-矩阵的逆矩阵的无穷大范数上界新的估计式,进而给出严格对角占优M-矩阵的最小特征值下界的估计式.新估计式改进了已有文献的结果.     

A NOTE ON THE RELATIVE CANONICAL IMAGE OF A NON－HYPERELLIPTIC FIBRATION OF GENUS 4

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Fibrations by nonsmooth genus three curves in characteristic three

Bertini’s theorem on variable singular points may fail in positive characteristic, as was discovered by Zariski in 1944. In fact, he found fibrations by nonsmooth curves. In this work we continue to classify this phenomenon in characteristic three by constructing a two-dimensional algebraic fibration by nonsmooth plane projective quartic curves, that is universal in the sense that the data about some fibrations by nonsmooth plane projective quartics are condensed in it. Our approach has been motivated by the close relation between it and the theory of regular but nonsmooth curves, or equivalently, nonconservative function fields in one variable. Actually, it also provides an understanding of the interesting effect of the relative Frobenius morphism in fibrations by nonsmooth curves. In analogy to the Kodaira-Néron classification of special fibers of minimal fibrations by elliptic curves, we also construct the minimal proper regular model of some fibrations by nonsmooth projective plane quartic curves, determine the structure of the bad fibers, and study the global geometry of the total spaces.     

Fibrations by curves with more than one nonsmooth point

Bertini’s theorem on variable singular pointsmay fail in positive characteristic, as was discovered by Zariski in 1944. In fact, he found fibrations by nonsmooth curves. In this work we continue to classify this phenomenon in characteristic three by constructing the first example, rising in the literature, of fibrations with more than one nonsmooth point. Our approach has been motivated by the close relation between it and the theory of regular but nonsmooth curves, or equivalently, nonconservative function fields in one variable. In analogy to the Kodaira-Néron classification of special fibers of minimal fibrations by elliptic curves, we also construct the minimal proper regular model of some fibrations by nonsmooth projective plane quartic curves and determine the structure of the bad fibers.     

A characterisation of elementary fibrations

In the categorical approach to logic proposed by Lawvere, which systematically uses adjoints to describe the logical operations, equality is presented in the form of a left adjoint to reindexing along diagonal arrows in the base. Taking advantage of the modular perspective provided by category theory, one can look at those Grothendieck fibrations which sustain just the structure of equality, the so-called elementary fibrations, aka fibrations with equality.The present paper provides a characterisation of elementary fibrations which is a substantial generalisation of the one already available for faithful fibrations. The characterisation is based on a particular structure in the fibres which may be understood as proof-relevant equality predicates equipped with a principle of indiscernibility of identicals à la Leibniz. We exemplify this structure for several classes of fibrations, in particular, for fibrations used in the semantics of the identity type of Martin-Löf type theory. We close the paper discussing some fibrations related to Hofmann and Streicher's groupoid model of the identity type and showing that one of them is elementary.     

On certain Mordell-Weil lattices of hyperelliptic type on rational surfaces

We study a class of rational hyperelliptic fibrations that can serve as a natural higher-genus analogue of rational elliptic fibrations from the standpoint of Mordell-Weil lattices. As a corollary, we obtain certain generalizations of the root lattices. We also describe the torsion part. Translated from Itogi Nauki i Tekhniki, Seriya Sovremennaya Matematika i Ee Prilozheniya. Tematicheskie Obzory. Vol. 62, Algebraic Geometry-10, 1999.     

Fibrations of topological stacks

In this note we define fibrations of topological stacks and establish their main properties. When restricted to topological spaces, our notion of fibration coincides with the classical one. We prove various standard results about fibrations (long exact sequence for homotopy groups, Leray–Serre and Eilenberg–Moore spectral sequences, etc.). We prove various criteria for a morphism of topological stacks to be a fibration, and use these to produce examples of fibrations. We prove that every morphism of topological stacks factors through a fibration and construct the homotopy fiber of a morphism of topological stacks. As an immediate consequence of the machinery we develop, we also prove van Kampen?s theorem for fundamental groups of topological stacks.     

Indecomposability of certain Lefschetz fibrations

We prove that Lefschetz fibrations admitting a section of square cannot be decomposed as fiber sums. In particular, Lefschetz fibrations on symplectic 4-manifolds found by Donaldson are indecomposable. This observation also shows that symplectic Lefschetz fibrations are not necessarily fiber sums of holomorphic ones.

     

Fibrations of Genus Two on Complex Surfaces

This work is devoted to the study of fibrations of genus 2 by using as its main tool the theory of singular holomorphic foliations. In particular we obtain a sharp differentiable version of Matsumoto–Montesinos theory. In the case of isotrivial fibrations, these methods are powerful enough to provide a detailed global picture of the both the ambient surface and of the structure of the fibrations itself.     

Kodaira fibrations and beyond: methods for moduli theory

Kodaira fibred surfaces are remarkable examples of projective classifying spaces, and there are still many intriguing open questions concerning them, especially the slope question. The topological characterization of Kodaira fibrations is emblematic of the use of topological methods in the study of moduli spaces of surfaces and higher dimensional complex algebraic varieties, and their compactifications. Our tour through algebraic surfaces and their moduli (with results valid also for higher dimensional varieties) deals with fibrations, questions on monodromy and factorizations in the mapping class group, old and new results on Variation of Hodge Structures, especially a recent answer given (in joint work with Dettweiler) to a long standing question posed by Fujita. In the landscape of our tour, Galois coverings, deformations and rigid manifolds (there are by the way rigid Kodaira fibrations), projective classifying spaces, the action of the absolute Galois group on moduli spaces, stand also in the forefront. These questions lead to interesting algebraic surfaces, for instance remarkable surfaces constructed from VHS, surfaces isogenous to a product with automorphisms acting trivially on cohomology, hypersurfaces in Bagnera-de Franchis varieties, Inoue-type surfaces.     

On Nonrational Fibers of del Pezzo Fibrations over Curves

We consider threefold del Pezzo fibrations over a curve germ whose central fiber is nonrational. Under the additional assumption that the singularities of the total space are at worst ordinary double points, we apply a suitable base change and show that there is a one-to-one correspondence between such fibrations and certain nonsingular del Pezzo fibrations equipped with a cyclic group action.