Existence of the primitive Weierstrass gap sequences on curves of genus 9

We show that for any possible Weierstrass gap sequenceL on a curve of genus 9 with twice the smallest positive non-gap > the largest gap there exists a pointed non-singular curve (C, P) over an algebraically closed field of characteristic 0 such that the gap sequence atP isL.     

Irrationality of Motivic series of Chow varieties

In this paper we extend the Euler–Chow series for Chow varieties to Chow motives. In both series it is very natural to ask when the series is rational. We give an example where the extended series is not rational. Partially supported by program JSPS-CONCYT.     

The subvariety lattice of the join of two semigroup varieties

The join A ∨ B of two semigroup varieties A and B is investigated. The latrine of subvarieties of A ∨ B is completely described, It is shown that this lattice is finite and non-modular and that all varieties in it are finitely based and finitely generated.     

实分片代数曲线的某些研究

分片代数曲线作为二元样条函数的零点集合是经典代数曲线的推广. 利用代数的基本知识, 本文对实分片代数曲线的基本性质进行了初步讨论, 并且将实分片代数曲线与相应的二元样条分类进行讨论. 最后, 对实分片代数曲线上的孤立点进行了研究.     

Identifying quadric bundle structures on complex projective varieties

In this paper we characterize smooth complex projective varieties that admit a quadric bundle structure on some dense open subset in terms of the geometry of certain families of rational curves.      

Cohomologie des variétés de Deligne-Lusztig

We study the cohomology of Deligne-Lusztig varieties with aim the construction of actions of Hecke algebras on such cohomologies, as predicted by the conjectures of Broué, Malle and Michel ultimately aimed at providing an explicit version of the abelian defect conjecture. We develop the theory for varieties associated to elements of the braid monoid and partial compactifications of them. We are able to compute the cohomology of varieties associated to (possibly twisted) rank 2 groups and powers of the longest element w₀ (some indeterminacies remain for G₂). We use this to construct Hecke algebra actions on the cohomology of varieties associated to w₀ or its square, for groups of arbitrary rank. In the subsequent work [F. Digne, J. Michel, Endomorphisms of Deligne-Lusztig varieties, Nagoya J. Math. 183 (2006)], we construct actions associated to more general regular elements and we study their traces on cohomology.     

Defining equations of the universal abelian surfaces with level three structure

In this paper we write down the defining equations of abelian surface with level three structures explicitly, and we see that their coefficients are given by Siegel modular forms of level three with some characters.     

用多消失矩最优小波包基改进虹膜识别

采用层叠算法求出尺度函数和小波函数的离散采样序列的逼进，将不具有基函数解析表达式的母小波用于虹膜特征提取，并利于实现连续小波包变换.针对虹膜光学识别应用背景，提出采用基于连续小波包变换的多消失矩联合最优小波包基来改进特征图像相关识别的最优基，并用统计识别方法进行后处理以增强算法适应性，同时提出通过体全息相关系统来实现，以发挥光学高并行性的优势，模拟结果表明可获得比已有方法更高的识别率.     

Chtoucas de Drinfeld et correspondance de Langlands

One proves Langlands’ correspondence for GL _r over function fields. This is a generalization of Drinfeld’s proof in the case of rank 2 : Langlands’ correspondence is realized in ℓ-adic cohomology spaces of the modular varieties classifying rank r Drinfeld shtukas. Oblatum 13-X-2000 & 7-VI-2001?Published online: 12 October 2001     

Arithmetic Interpretability Types of Varieties and Some Additive Problems with Primes

We deal with varieties with one basic operation f(x₁,...,x_n) and one defining identity f(x₁,..., x_n) = f(x_π(1),...,x_π(n)), where π is a permutation whose cyclic set consists of distinct primes p₁,...,p_r, with the sum p₁+...+p_r = n. Their interpretability types, together with the greatest element 1 in a lattice ^int, are said to be arithmetic. It is proved that the arithmetic types constitute a distributive lattice _ar, which is dual to a lattice Sub _fΠ of finite subsets of the set Π of all primes. It is shown that for n ⩾ 2, the poset _ar( _n) of arithmetic types defined by permutations in _n, for n fixed, is a lattice iff n = 2, 3, 4, 6, 8, 9, 11. __________ Translated from Algebra i Logika, Vol. 44, No. 5, pp. 622–630, September–October, 2005.