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1.
We define a quasi–projective reduction of a complex algebraic variety X to be a regular map from X to a quasi–projective variety that is universal with respect to regular maps from X to quasi–projective varieties. A toric quasi–projective reduction is the analogous notion in the category of toric varieties.
For a given toric variety X we first construct a toric quasi–projective reduction. Then we show that X has a quasi–projective reduction if and only if its toric quasi–projective reduction is surjective. We apply this result
to characterize when the action of a subtorus on a quasi–projective toric variety admits a categorical quotient in the category
of quasi–projective varieties.
Received October 29, 1998; in final form December 28, 1998 相似文献
2.
A. Albouy 《Regular and Chaotic Dynamics》2008,13(6):525-542
We show that there exists a projective dynamics of a particle. It underlies intrinsically the classical particle dynamics
as projective geometry underlies Euclidean geometry. In classical particle dynamics a particle moves in the Euclidean space
subjected to a potential. In projective dynamics the position space has only the local structure of the real projective space.
The particle is subjected to a field of projective forces. A projective force is not an element of the tangent bundle to the position space, but of some fibre bundle isomorphic to
the tangent bundle.
These statements are direct consequences of Appell’s remarks on the homography in mechanics, and are compatible with similar
statements due to Tabachnikov concerning projective billiards. When we study Euclidean geometry we meet some particular properties
that we recognize as projective properties. The same is true for the dynamics of a particle. We show that two properties in
classical particle dynamics are projective properties. The fact that the Keplerian orbits close after one turn is a consequence
of a more general projective statement. The fact that the fields of gravitational forces are divergence free is a projective
property of these fields.
相似文献
3.
4.
O. A. Starikova 《Journal of Mathematical Sciences》2012,187(2):177-186
Relatively recent and new results on the enumeration of classes of projective congruent quadrics and classes of projective equivalent quadrics of projective spaces over a local ring R = 2R with nilpotent principal maximal ideal are reflected in the paper. For the case of the basic ring R with nonprincipal maximal ideal, the enumerations of quadrics of projective plane are given up to projective equivalence. 相似文献
5.
Hajime Kaji 《Geometriae Dedicata》2009,139(1):75-82
In projective algebraic geometry, various pathological phenomena in positive characteristic have been observed by several authors. Many of those phenomena concerning the behavior of embedded tangent spaces seem to be controlled by the separability of (the extension of function fields defined by) the Gauss map, or by the reflexivity with respect to the projective dual for a projective variety. The purpose of this paper is to survey the studies on the relationship between the separability of the Gauss map and the reflexivity for a projective variety: Is the separability of the Gauss map equivalent to the reflexivity for a projective variety? 相似文献
6.
《Chaos, solitons, and fractals》2001,12(13):2517-2535
The projective dimensional analysis based on the projective extension of scaling group and projective dimensional function is presented. We study the notion of self-similarity based on the physical quantities and not on topology. The projective analog of the classical theorem-π has been formulated in terms of (projective) numerical invariants. The additivity dimensions replacing fractal dimension are briefly discussed. Intuitive examples illustrate presented ideas. 相似文献
7.
本文研究和刻画了射影Ricci平坦的Kropina度量.利用Kropina度量的S-曲率和Ricci曲率的公式,得到了Kropina度量的射影Ricci曲率公式.在此基础上得到了Kropina度量是射影Ricci平坦度量的充分必要条件.进一步,作为自然的应用,本文研究和刻画了由一个黎曼度量和一个具有常数长度的Killing 1-形式定义的射影Ricci平坦的Kropina度量,也刻画了具有迷向S-曲率的射影Ricci平坦的Kropina度量.在这种情形下,Kropina度量是Ricci平坦度量. 相似文献
8.
Our paper deals with the covering number of finite projective planes which is related to an unsolved question of P. Erdös. An integer linear programming (ILP) formulation of the covering number of finite projective planes is introduced for projective planes of given orders. The mathematical programming based approach for this problem is new in the area of finite projective planes. Since the ILP problem is NP-hard and may involve up to 360.000 boolean variables for the considered problems, we propose a heuristic based on Simulated Annealing. The computational study gives a new insight into the structure of projective planes and their (minimal) blocking sets. This computational study indicates that the current theoretical results may be improved. 相似文献
9.
In the present article, the authors have proposed a modified projective adaptive synchronization technique for fractional‐order chaotic systems. The adaptive projective synchronization controller and identification parameters law are developed on the basis of Lyapunov direct stability theory. The proposed method is successfully applied for the projective synchronization between fractional‐order hyperchaotic Lü system as drive system and fractional‐order hyperchaotic Lorenz chaotic system as response system. A comparison between the effects on synchronization time due to the presence of fractional‐order time derivatives for modified projective synchronization method and proposed modified adaptive projective synchronization technique is the key feature of the present article. Numerical simulation results, which are carried out using Adams–Boshforth–Moulton method show that the proposed technique is effective, convenient and also faster for projective synchronization of fractional‐order nonlinear dynamical systems. Copyright © 2013 John Wiley & Sons, Ltd. 相似文献
10.
Klaus Metsch 《Journal of Geometry》1990,37(1-2):128-141
We classify all finite linear spaces without three mutually parallel lines. Apart from two exceptions, such a space is necessarily a generalized projective plane, a simple extension of a generalized projective plane, or a complete inflated affine plane with a generalized projective plane at infinity.Dedicated to Giuseppe Tallini on the occasion of his 60th birthday 相似文献
11.
Antonio Maschietti 《Journal of Geometry》1992,44(1-2):107-116
In this paper, we investigatec-sets in 2-designs, with particular regard to sets of type (0,n) in projective planes. In particular, we associate a Hadamard design to a hyperoval of a projective plane of even orderq and we investigate some properties of its lines. This gives information on the order of the projective plane. 相似文献
12.
Thomas Mettler 《Monatshefte für Mathematik》2014,174(4):599-616
We derive necessary conditions for a complex projective structure on a complex surface to arise via the Levi-Civita connection of a (pseudo-)Kähler metric. Furthermore we show that the (pseudo-)Kähler metrics defined on some domain in the projective plane which are compatible with the standard complex projective structure are in one-to-one correspondence with the hermitian forms on \(\mathbb {C}^3\) whose rank is at least two. This is achieved by prolonging the relevant finite-type first order linear differential system to closed form. Along the way we derive the complex projective Weyl and Liouville curvature using the language of Cartan geometries. 相似文献
14.
Vic Patrangenaru Mingfei Qiu Marius Buibas 《Methodology and Computing in Applied Probability》2014,16(2):485-506
In this article, we extend mean 3D projective shape change in matched pairs to independent samples. We provide a brief introduction of projective shapes of spatial configurations obtained from their digital camera images, building on previous results of Crane and Patrangenaru (J Multivar Anal 102:225–237, 2011). The manifold of projective shapes of k-ads in 3D containing a projective frame at five given landmark indices has a natural Lie group structure, which is inherited from the quaternion multiplication. Here, given the small sample size, one estimates the mean 3D projective shape change in two populations, based on independent random samples of possibly different sizes using Efron’s nonparametric bootstrap. This methodology is applied in three relevant applications of analysis of 3D scenes from digital images: visual quality control, face recognition, and scene recognition. 相似文献
15.
A generalization of Kaplansky's theorem on projective modules over local rings is used to show that every projective diagram over a poset is free. 相似文献
16.
Qihong XIE 《数学年刊B辑(英文版)》2011,32(5):741-748
The author gives a characterization of counterexamples to the Kodaira-Ramanujam vanishing theorem on smooth projective surfaces
in positive characteristic. More precisely, it is reproved that if there is a counterexample to the Kodaira-Ramanujam vanishing
theorem on a smooth projective surface X in positive characteristic, then X is either a quasi-elliptic surface of Kodaira dimension 1 or a surface of general type. Furthermore, it is proved that up
to blow-ups, X admits a fibration to a smooth projective curve, such that each fiber is a singular curve. 相似文献
17.
Rigoberto Flórez 《Discrete Mathematics》2009,309(8):2365-2372
We study a generalization of the concept of harmonic conjugation from projective geometry and full algebraic matroids to a larger class of matroids called harmonic matroids. We use harmonic conjugation to construct a projective plane of prime order in harmonic matroids without using the axioms of projective geometry. As a particular case we have a combinatorial construction of a projective plane of prime order in full algebraic matroids. 相似文献
18.
Ivo Düntsch 《Algebra Universalis》1982,14(1):167-180
Some properties of projective stone algebras are exhibited, which are connected with the ordered set of prime ideals. From
this we derive a simple characterization of finite projective Stone algebras, and of those projective Stone algebras, whose
centre is a projective Boolean algebra, and whose dense set is a projective Stone algebras, whose centre is a projective Boolean
algebra, and whose dense set is a projective distributive lattice. Finally, we give some conditions under which a Stone algebra
has no chains of type λ, where λ is an infinite regular cardinal.
The results of this paper are part of the author's Ph.D. Thesis written under the direction of S. Koppelberg. The author wishes
to express his gratitude to Prof. Koppelberg for her guidance and her patience.
Presented by K. A. Baker. 相似文献
19.
Rodrigo A. H. M. Cabral 《Mathematische Nachrichten》2023,296(2):534-551
We establish the notion of a “projective analytic vector”, whose defining requirements are weaker than the usual ones of an analytic vector, and use it to prove generation theorems for one-parameter groups on locally convex spaces. More specifically, we give a characterization of the generators of strongly continuous one-parameter groups which arise as the result of a projective limit procedure, in which the existence of a dense set of projective analytic vectors plays a central role. An application to strongly continuous Lie group representations on Banach spaces is given, with a focused analysis on concrete algebras of functions and of pseudodifferential operators. 相似文献
20.
Christopher Manon 《Journal of Algebraic Combinatorics》2010,31(4):467-489
We study presentations for subalgebras of invariants of the coordinate algebras of binary symmetric models of phylogenetic
trees studied by Buczynska and Wisniewski in (J. Eur. Math. Soc. 9:609–635, 2007). These algebras arise as toric degenerations of projective coordinate rings of the moduli of weighted points on the projective
line, and projective coordinate rings of the moduli of quasiparabolic semisimple rank two bundles on the projective line. 相似文献