Automorphisms of a Generic Jacobian Kummer Surface

For a generic quartic surface F in ³ with sixteen nodes, we shall prove that every birational automorphism of F is induced by a Cremona transformation of ³.     

Commuting Rank 2 Differential Operators Corresponding to a Curve of Genus 2

We construct commuting rank 2 formally self-adjoint ordinary differential operators corresponding to a curve of genus 2.     

亏格为4黎曼曲面上循环群作用的拓扑分类

本文主要考虑循环群作用 Riemann曲面的分类问题 ,我们列出了所有的循环群作用亏格为 4Riem ann曲面的拓扑分类和弱拓扑分类     

Curves on a Kummer Surface in ℙ3, I

In this paper the asymptotic behaviour of the solutions of x' = A(t)x + h(t,x) under the assumptions of instability is studied, A(t) and h(t,x) being a square matrix and a vector function, respectively. The conditions for the existence of bounded solutions or solutions tending to the origin as t → ∞ are obtained. The method: the system is recasted to an equation with complex conjugate coordinates and this equation is studied by means of a suitable Lyapunov function and by virtue of the Wazevski topological method. Applications to a nonlinear differential equation of the second order are given.     

Equivalent Separating Curves on Closed Surface of Genus 2

Let {A,B} be a complete system of the closed orientable surface F of genus 2. A simple closed curve C on F is separating with respect to (A, B) if it is disjoint from A∪B and it cuts F into two once-punctured tori X, Y with A(?)X, B(?)Y. Letγbe a simple closed curve on F which is disjoint from A∪B and intersects C essentially in two points. In this paper, we show that up to isotopy, {hnγ(C):n∈Z} is the set containing all the simple closed curves on F which is separating with respect to (A,B), where hγis the Dehn twist alongγon F. This also shows how two simple closed curves on F which are separating with respect to (A,B) are related. The result can be applied to yield all Haken spheres of a Heegaard splitting V∪F W which are weakly equivalent to a given Heken sphere of the splitting.     

On the Genus of a Finite Classical Group

Let G be a finite group acting faithfully and transitively ona set of size m, and let E = {x₁, ..., x_k} be a generatingset for G with x₁x₂...x_k = 1. If x G has cycles of length r₁,..., r_l in its action on , define . Then the genus g = g(G, , E) is defined by 1991 Mathematics Subject Classification 20B25, 20G40,30F99.     

关于曲面的有界性及第二类曲面积分的教学实践

给出了高等数学范畴的曲面有界性定义;总结了对高等数学的教学难点之一,第二类曲面积分的教学实践,使得在解决这一老大难问题时思路清晰,可操作性强,教学效果较好.     

曲面上曲线复形中边的距离

Let S be a closed orientable surface of genus g ≥ 2,and C（S）the curve complex of S.In the paper,we introduce the concepts of 2-path between edges in C（S）,which can be regarded as an analogue to the edge path between vertices in C（S）.We show that C（S）is 2P-connected,and the 2-diameter of C（S）is infinite.     

Curves of Genus Three in Characteristic Two

For an algebraic nonsingular nonhyperelliptic complete curve of genus three defined over a field of characteristic two we show that the number of canonical Weierstrass points is one of the following: 24, 21, 20, 18, 17, 16, 15, 12, 11, 6 or 5. In most cases, we give also an explicit equation for the curve with the given number of Weierstrass points.     

基于特征峰识别的弹头痕迹自动比对方法

针对2009年全国研究生数学建模竞赛B题,以自动比对方法的智能性,自动性和可操作性为出发点,以构建子弹头特征峰数据库,搭建子弹头自动比对系统为目标,对枪弹头痕迹的自动比对问题展开了研究.类比搜索引擎的关键词搜索技术建立了基于图形的特征峰搜索技术,实现了弹头痕迹的智能比对.     

On a Universal Mapping Class Group of Genus Zero

The aim of this paper is to introduce a group containing the mapping class groups of all genus zero surfaces. Roughly speaking, such a group is intended to be a discrete analogue of the diffeomorphism group of the circle. One defines indeed a universal mapping class group of genus zero, denoted The latter is a nontrivial extension of the Thompson group V (acting on the Cantor set) by an inductive limit of pure mapping class groups of all genus zero surfaces. We prove that is a finitely presented group, and give an explicit presentation of it.     

There is a Group of Every Strong Symmetric Genus

Let G be a finite group. The strong symmetric genus ⁰(G) isthe minimum genus of any Riemann surface on which G acts, preservingorientation. For any non-negative integer g, there is at leastone group of strong symmetric genus g. For g2, one such grouphas the form Z_k x D_n for some k and n. 2000 Mathematics SubjectClassification 57M60 (primary), 20H10, 30F99 (secondary).     

The Two-Point Codes with the Designed Distance on a Hermitian Curve in Even Characteristic

In Homma M and Kim SJ [2], the authors considered two-point codes on a Hermitian curve defined over fields of odd characteristic. In this paper, we study the geometry of a Hermitian curve over fields of even characteristic and classify the two-point codes whose minimum distances agree with the designed ones.     

A Combinatorial Characterazition of the Fermat Cubic Surface in Characteristic 2

We study a particular geometry in characteristic 2. Let X be a cubic surface obtained from ² by means of blowing up with centersP ₁,...,P ₆. We prove that X is projectively equivalent to the Fermat cubic surface with equation x _i ³ if and only if each point of P ₁,..., P ₆ is the nucleus of the conic passing through the remaining five points.     

On the Number of Galois Points for a Plane Curve in Positive Characteristic

We study Galois points for a plane smooth curve C ? P ² of degree d ≥ 4 in characteristic p > 2. We generalize Yoshihara's result on the number of inner (resp., outer) Galois points to positive characteristic under the assumption that d ? 1 (resp., d ? 0) modulo p. As an application, we also find the number of Galois points in the case that d = p.     

On the Divided Power Algebra and the Symplectic Group in Characteristic 2

Let V be an even dimensional vector space over a field K of characteristic 2 equipped with a nondegenerate alternating bilinear form f. The divided power algebra DV is considered as a complex with differential defined from f. We examine the cohomology modules as representations of the corresponding symplectic group.     

Involutions of a Clifford Algebra Induced by Involutions of Orthogonal Group in Characteristic 2

Among the involutions of a Clifford algebra, those induced by the involutions of the orthogonal group are the most natural ones. In this work, several basic properties of these involutions, such as the relations between their invariants, their occurrences, and their decompositions, are investigated.