On Birational Geometry of Algebraic Varieties

论代数簇的双有理几何

• 批准号: 07454003
• 负责人: SAKAI Fumio
• 金额: $ 4.16万
• 依托单位: Saitama University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (B)
• 财政年份: 1995
• 资助国家: 日本
• 起止时间: 1995 至 1996
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-07454003/
• 关键词: cyclic covering; Betti number; algebraic surface; singularities; projective space; modular group; monifold; foliation; Bellman方程式; 4元数; 量子束; 概接触構造

Sakai generalizel Zarishi's theorem on cyolic coverings of the projective plane to the cyclic coveings of algebraic surfaces under the hyposhesis that the degree of the covering's a power of a prime number and the Branch euwe could be reducible. He also improve an estimate of the total Milnor member of plane cuwes with simple singulinties.Okumura obtained a sufficient condition which guaranties that a CR-submeniforld of a complex projective opere is a product of odd dimensional sphers.Takeuchi classified all moduler subgroups G of the modular group SL_2 (TS) which has signatine (o ; e_1, e_2, e_3). Moreour, he gave the matrix forms.Koike considored the solution of a Bell monequotion. He obtoineda sufficient condition for the uniqueness of the solution.Egashira studied C^2-class codimeusion one foliatiation on a compact monifold.

Sakai把Zarishi关于射影平面的循环覆盖的定理推广到代数曲面的循环覆盖上，假设覆盖的次数是素数的幂，并且分支是可约的. Okumura得到了复射影算子的CR-子群是奇数维球面的积的一个充分条件，Takeuchi对模群SL_2（TS）中具有符号（o ; e_1，e_2，e_3）的所有模子群G进行了分类。此外，他还给出了矩阵的形式。小池考虑了贝尔方程的解。Egashira研究了紧致流形上的C^2-类codime-one叶理化。

项目成果

S. Egashira: "Expansion groth of smooth codimension-one foliations" J. Math. Soc. Japan. 48. 109-123 (1996)

S. Egashira：“光滑余维一叶状结构的膨胀增长”J. Math。

Sakai, F.: "Generaligation of Zariski's theorem on the inegularity of cyclic coverings" Proc.Conference (T.I.T). 99-102 (1996)

Sakai, F.：“Zariski 循环覆盖不规则性定理的概括”Proc.Conference (T.I.T)。

Sakai, F.: "The inegulenty of cyclic coverings and singularities of plane cuwes" Proc.Conference (Saitama Univ.). 118-132 (1996)

Sakai, F.：“平面立方体的循环覆盖和奇点的不恰当性”Proc.Conference（埼玉大学）。

K.Takeuchi: "Subgroups of the modulargroups with signeture(o;e_1,e_2,e_3)" Saitoma Math,J.14. 55-78 (1996)

K.Takeuchi：“带有签名的模群的子群(o;e_1,e_2,e_3)”Saitoma Math，J.14。

T. Sakurai: "Analytic hypoellipticity and local solvability for a class of pseudo-differential operators with symplectic characteristics" Banach Center Publications. (1995)

T. Sakurai：“一类具有辛特征的伪微分算子的解析亚椭圆性和局部可解性”Banach Center Publications。