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Some Kinds of sheaf Control Problems for Control Systems

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Applied Mathematics 2012年第1期3卷 39-44页

作者： Nguyen Dinh Phu Phan Van Tri Faculty of Mathematics and Computer Science Vietnam National University

Recently, the field of differential equations has been studying in a very abstract method. Instead of considering the behaviour of one solution of a differential equation, one studies its sheaf-solutions in many kinds of properties, for example, the problems of existence, comparison,... of sheaf solutions. In this paper we study some of the problems of controllability for sheaf solutions of control systems.

关键词： Control Systems sheaf Solutions Control Theory

On Tubular Tilting Objects in the Stable Category of Vector Bundles

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Acta Mathematica Sinica,English Series 2019年第4期35卷 494-512页

作者： Jian Min CHEN Ya Nan LIN Shi Quan RUAN School of Mathematical Sciences Xiamen University

The present paper focuses on the study of the stable category of vector bundles for the weighted projective lines of weight triple. We find some important triangles in this category and use them to construct tilting o... 详细信息

关键词： Tilting sheaf weighted projective line stable category cluster category tubular algebra

An interpolation characterization of domains of holomorphy

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Chinese Science Bulletin 1997年第23期42卷 1954-1956页

作者： Liu, TS Liu, CW Zhang, WJ Univ Sci & Technol China Dept Math Hefei 230026 Peoples R China

1 Main resultA connected open set Ω Cn is called a domain of holomorphy, if there do not exist nonemptyopen sets Ω1, Ω2 with Ω2 connected, Ω1 Ω2∩Ω, Ω2 Ω, so that for every u that is holo-morphic on Ω there is a u2 holomorphic on Ω2 with u=u2 on Ω1. This definition is compli-cated. Generally speaking, a domain of holomorphy is a domain of definition of holomorphicfunctions in the sense that there exists a holomorphic function on Ω that cannot be holomor-phically continued to any slightly large open set. Domains of holomorphy play a very importantrole in the theory of several complex variables. There are many different characterizations fordomains of holomorphy--geometrical, analytical or algebraical, each takes its different effi-cient functions in treating various concrete problems of several complex variables （see ref.[1], for example）. In this note, we use the skills of sheaf theory to give a characterization ofdomains of holomorphy by mealls of some interpolation property.

关键词： domains of holomorphy interpolation coherent analytic sheaf cohomology.

Some Results on Special Stable Vector Bundles of Rank 3 on Algebraic Curves

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Acta Mathematica Sinica,English Series 2008年第3期24卷 417-430页

作者： Bo Han FANGi Xiao Jiang TAN Wei Yi ZHANG School of Mathematical Sciences Peking University Beijing 100871 P. R. China The research is supported by President Foundation of Peking University

The authors discuss the existence and classification of stable vector bundles of rank 3, with 2 3 or 4 linearly independent holomorphic sections. The sets of all such bundles are denoted by ω3^2,d and w3 respectively. Our argument leads to sufficient and necessary conditions for the existence of both kinds of bundles. The conclusion is very interesting because of its contradiction to the conjectured dimension formula of stable bundles. Finally, we give a preliminary classification of ω3^2,4 and a complete discussion on the structure of ω3^3,2/3g＋2.

关键词： algebraic curves stable vector bundles sheaf conjectured dimension formula

The moduli space of Hopf surfaces

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Science China Mathematics 1995年第9期38卷 1049-1059页

作者：李庆忠张锦豪 Institute of Mathematics Chinese Academy of Sciences Beijing 100080 China Department of Mathematics Fudan University Shanghai 200433 China

The moduli space of complex structures on S1×S3/H) is studied, where H U(2) is a fi-nite Abelian group whose action is properly discontinuous and free on S3.

关键词： deformation of complex structures cohomology with coefficients in a sheaf Kodaira-Spencer mapping.

Penrose Transform on Induced DG/H-Modules and Their Moduli Stacks in the Field Theory

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Advances in Pure Mathematics 2013年第2期3卷 246-253页

作者： Francisco Bulnes Department of Research in Mathematics and Engineering Tecnológico de Estudios Superiores de Chalco Chalco Mexico

We consider generalizations of the Radon-Schmid transform on coherent DG/H-Modules, with the intention of obtaining the equivalence between geometric objects (vector bundles) and algebraic objects (D-Modules) characterizing conformal classes in the space-time that determine a space moduli [1] on coherent sheaves for the securing solutions in field theory [2]. In a major context, elements of derived categories like D-branes and heterotic strings are considered, and using the geometric Langlands program, a moduli space is obtained of equivalence between certain geometrical pictures (non-conformal world sheets [3]) and physical stacks (derived sheaves), that establishes equivalence between certain theories of super symmetries of field of a Penrose transform that generalizes the implications given by the Langlands program. With it we obtain extensions of a cohomology of integrals for a major class of field equations to corresponding Hecke category.

关键词： Penrose Transform Coherent G-Quasi-Equivariant D-Modules Hecke sheaf Moduli Stacks Moduli Spaces

Penrose Transform on D-Modules, Moduli Spaces and Field Theory

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Advances in Pure Mathematics 2012年第6期2卷 379-390页

作者： Francisco Bulnes Department of Research in Mathematics and Engineering Technological Institute of High Studies of Chalco Chalco Mexico

We consider a generalization of the Radon-Schmid transform on coherent D-modules of sheaves of holomorphic complex bundles inside a moduli space, with the purpose of establishing the equivalences among geometric objects (vector bundles) and algebraic objects as they are the coherent D-modules, these last with the goal of obtaining conformal classes of connections of the holomorphic complex bundles. The class of these equivalences conforms a moduli space on coherent sheaves that define solutions in field theory. Also by this way, and using one generalization of the Penrose transform in the context of coherent D-modules we find conformal classes of the space-time that include the heterotic strings and branes geometry.

关键词： Penrose Transform Coherent D-Modules Derived sheaf Moduli Space Conformal Classes Heterotic Strings