共查询到20条相似文献,搜索用时 203 毫秒
1.
The application of the method of multiplier ideal sheaves to effective problems in algebraic geometry is briefly discussed. Then its application to the deformational invariance of plurigenera for general compact algebraic manifolds is presented and discussed. Finally its application to the conjecture of the finite generation of the canonical ring is explored, and the use of complex algebraic geometry in complex Neumann estimates is discussed.
相似文献2.
O. Ya. Viro 《Proceedings of the Steklov Institute of Mathematics》2011,273(1):252-282
We introduce a binary operation over complex numbers that is a tropical analog of addition. This operation, together with
the ordinary multiplication of complex numbers, satisfies axioms that generalize the standard field axioms. The algebraic
geometry over a complex tropical hyperfield thus defined occupies an intermediate position between the classical complex algebraic
geometry and tropical geometry. A deformation similar to the Litvinov-Maslov dequantization of real numbers leads to the degeneration
of complex algebraic varieties into complex tropical varieties, whereas the amoeba of a complex tropical variety turns out
to be the corresponding tropical variety. Similar tropical modifications with multivalued additions are constructed for other
fields as well: for real numbers, p-adic numbers, and quaternions. 相似文献
3.
As a piecewise polynomial with a certain smoothness, the spline plays an important role in computational geometry. The algebraic variety is the most important subject in classical algebraic geometry. As the zero set of multivariate splines, the piecewise algebraic variety is a generalization of the algebraic variety. In this paper, the correspondence between piecewise algebraic varieties and spline ideals is discussed. Furthermore, Hilbert’s Nullstellensatz for the piecewise algebraic variety is also studied. 相似文献
4.
《Journal of Computational and Applied Mathematics》2012,236(5):793-800
As a piecewise polynomial with a certain smoothness, the spline plays an important role in computational geometry. The algebraic variety is the most important subject in classical algebraic geometry. As the zero set of multivariate splines, the piecewise algebraic variety is a generalization of the algebraic variety. In this paper, the correspondence between piecewise algebraic varieties and spline ideals is discussed. Furthermore, Hilbert’s Nullstellensatz for the piecewise algebraic variety is also studied. 相似文献
5.
Given a generic semidefinite program, specified by matrices with rational entries, each coordinate of its optimal solution
is an algebraic number. We study the degree of the minimal polynomials of these algebraic numbers. Geometrically, this degree
counts the critical points attained by a linear functional on a fixed rank locus in a linear space of symmetric matrices.
We determine this degree using methods from complex algebraic geometry, such as projective duality, determinantal varieties,
and their Chern classes. 相似文献
6.
We develop the geometry of folding paths in Outer space and, as an application, prove that the complex of free factors of a free group of finite rank is hyperbolic. 相似文献
7.
《Journal of Number Theory》1986,22(2):147-160
This paper discusses an application of Minkowski's theory of the successive minima in the geometry of numbers to the problem of the approximation of an algebraic or transcendental number a by algebraic numbers. I consider for simplicity only real numbers a. However, it is obvious that an analogous theory can be established for complex numbers, and also for p-adic numbers, as well as for the field of formal ascending or descending Laurent series with coefficients in an arbitrary field. 相似文献
8.
应用逼近方法建立了一个关于复数代数无关性的一般性判别法则,并用来研究某些缺项级数在代数点和超越点上值的代数无关性. 相似文献
9.
Yanbin Yin & Ling Liu 《数学研究通讯:英文版》2016,32(2):111-116
Generalized complex geometry is a new kind of geometrical structure which contains complex and symplectic geometry as its special cases. This paper gives the equivalence between the integrable conditions of a generalized almost complex structure in big bracket formalism and those in the general framework. 相似文献
10.
B. Plotkin 《Journal of Mathematical Sciences》2006,137(5):5049-5097
In every variety of algebras Θ, we can consider its logic and its algebraic geometry. In previous papers, geometry in equational
logic, i.e., equational geometry, has been studied. Here we describe an extension of this theory to first-order logic (FOL).
The algebraic sets in this geometry are determined by arbitrary sets of FOL formulas. The principal motivation of such a generalization
lies in the area of applications to knowledge science. In this paper, the FOL formulas are considered in the context of algebraic
logic. For this purpose, we define special Halmos categories. These categories in algebraic geometry related to FOL play the
same role as the category of free algebras Θ0 play in equational algebraic geometry. This paper consists of three parts. Section 1 is of introductory character. The first
part (Secs. 2–4) contains background on algebraic logic in the given variety of algebras Θ. The second part is devoted to
algebraic geometry related to FOL (Secs. 5–7). In the last part (Secs. 8–9), we consider applications of the previous material
to knowledge science.
__________
Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 22, Algebra
and Geometry, 2004. 相似文献
11.
Algebraic independence by approximation method 总被引:4,自引:0,他引:4
Zhu Yaochen 《数学学报(英文版)》1998,14(3):295-302
By the use of approximation method a general criterion of algebraic independence of complex numbers is established. As its
application the algebraic independence of values of certain gap series at algebraic and transcendental points is given.
Subject supported by the National Natural Science Foundation of China 相似文献
12.
The notion of geometrical equivalence of two algebras, which is basic for this paper, is introduced in [5], [6]. It is motivated in the framework of universal algebraic geometry, in which algebraic varieties are considered in arbitrary varieties of algebras. Universal algebraic geometry (as well as classic algebraic geometry) studies systems of equations and its geometric images, i.e., algebraic varieties, consisting of solutions of equations. Geometrical equivalence of algebras means, in some sense, equal possibilities for solving systems of equations. In this paper we consider results about geometrical equivalence of algebras, and special attention is paied on groups (abelian and nilpotent). 相似文献
13.
The concepts of holomorphic sectional and bisectional curvatures for holomorphic vector bundles in complex Finsler geometry are used to characterize the concept of big vector bundles in algebraic geometry. 相似文献
14.
代数周(Chow)形式和代数结式是代数几何的基本概念,同时还是消去理论的强大工具.一个自然的想法是在微分代数几何中发展相应的周形式和结式理论.但是由于微分结构的复杂性,在本文的研究工作之前,微分结式只有部分结果,而微分周形式与稀疏微分结式理论一直没有得到发展.本文的主要结果包括:第一,发展一般(generic)情形的微分相交理论,作为应用,证明一般情形的微分维数猜想.第二,初步建立微分周形式理论.对不可约微分代数簇定义微分周形式并证明其基本性质,特别地,给出微分周形式的Poisson分解公式,引入微分代数簇的主微分次数这一不变量并证明一类微分代数闭链的周簇和周坐标的存在性.作为应用,首次严格定义微分结式,证明其基本性质.第三,初步建立稀疏微分结式理论.引入Laurent微分本性系统的概念,定义稀疏微分结式,证明其基本性质,特别地,引入微分环面簇的概念,给出稀疏微分结式阶数和次数界的估计,并基于此给出计算稀疏微分结式的单指数时间算法. 相似文献
15.
Shing-Tung Yau 《中国科学A辑(英文版)》2005,48(Z1)
This paper reviews the brief history of complex geometry and looks into its future. 相似文献
16.
The entropic discriminant is a non-negative polynomial associated to a matrix. It arises in contexts ranging from statistics and linear programming to singularity theory and algebraic geometry. It describes the complex branch locus of the polar map of a real hyperplane arrangement, and it vanishes when the equations defining the analytic center of a linear program have a complex double root. We study the geometry of the entropic discriminant, and we express its degree in terms of the characteristic polynomial of the underlying matroid. Singularities of reciprocal linear spaces play a key role. In the corank-one case, the entropic discriminant admits a sum of squares representation derived from the discriminant of a characteristic polynomial of a symmetric matrix. 相似文献
17.
Jonathan Rosenberg 《Transactions of the American Mathematical Society》2008,360(1):383-394
We introduce an analogue of the Novikov Conjecture on higher signatures in the context of the algebraic geometry of (nonsingular) complex projective varieties. This conjecture asserts that certain ``higher Todd genera' are birational invariants. This implies birational invariance of certain extra combinations of Chern classes (beyond just the classical Todd genus) in the case of varieties with large fundamental group (in the topological sense). We prove the conjecture under the assumption of the ``strong Novikov Conjecture' for the fundamental group, which is known to be correct for many groups of geometric interest. We also show that, in a certain sense, our conjecture is best possible.
18.
The noncommutative algebraic geometry has found fruitful applications in quantum geometry. Similar applications are expected to be found for its younger sister the noncommutative real algebraic geometry One of the basic results in real algebraic geometry is the Positivestellensatz. The original results of Dubois and Risler (see section 3.3 of [13]) have been extended in many directions. We refer to [14], [1], [2], [3] for commutative rings and [9], [4] for associative rings. The aim of this paper is to prove the higher level Posit ivstellensatz for noncommutative Noetherian rings. Our proof depends on the intersection theorem for orderings of higher level on skew fields ([11], Theorem 3.13). The general case of orderings of higher level on associative rings remains open. 相似文献
19.
LetX be a smooth complex algebraic surface such that there is a proper birational morphism/:X → Y withY an affine variety. Let Xhol be the 2-dimensional complex manifold associated toX. Here we give conditions onX which imply that every holomorphic vector bundle onX is algebraizable and it is an extension of line bundles. We also give an approximation theorem of holomorphic vector bundles
on Xhol (X normal algebraic surface) by algebraic vector bundles. 相似文献
20.
We construct the complex simple Lie algebras using elementary algebraic geometry. We use our construction to obtain a new
proof of the classification of complex simple Lie algebras that does not appeal to the classification of root systems. 相似文献