Geometry of branched Galois covers and number theory

1.分支伽罗瓦盖的构造问题和逆伽罗瓦问题：该项目主要由Tokunaga，Miyake和Tsuchihashi进行。德永主要研究了二维有限Galois覆盖。两篇关于2维有限Galois覆盖和有理椭圆曲面的论文正在出版中。他还表明，对2维通用伽罗瓦覆盖的研究可以归结为有限群的克雷莫纳表示的研究。关于这一主题的文件正在编写之中。Tsuchihashi利用环面几何构造了二面体群和对称群的伽罗瓦覆盖。他还研究了伽罗瓦覆盖P^2的普遍覆盖是polydisc。Miyake引入了定义在Q上的两条椭圆曲线，这两条曲线与某些三次域有关，并给出了所谓的“Mordell曲线”的显式简化形式。“2.开代数簇和奇点的拓扑：中村研究了Grothendieck-Teichmuller群。Tokunaga与萨拉戈萨大学的Artal Bartolo一起对Zakki κ-plets进行了研究，并给出了一个新的例子。这一结果即将公布。奥卡认真研究了平面六次曲线。Shimada对Picard数为21的超奇异K3曲面上有理二重点的所有可能构型进行了分类。

1.Construction problem of branched Galois covers and the inverse Galois problem : This project were manly carried out by Tokunaga, Miyake and Tsuchihashi. Tokunaga mainly studied on 2-dimensional versal Galois covers. Two papers on 2-dimensional versal Galois covers and rational elliptic surfaces are in press. Also he show that the study on 2-dimensional versal Galois covers is reduced to that of Cremona representations of finite groups. The paper on this subject is now in preparation. Tsuchihashi constructed versal Galois covers for dihedral groups and the symmetric group by using toric geometry. He also studied Galois covers of P^2 whose universal cover is polydisc. Miyake introduced two ellitpic curves defined over Q, which is related to certain cubic fields, and gave explicit short forms so-called "Mordell Cures."2.Topology of open algebraic varieties and singularities : Nakamura made investigation on Grothendieck-Teichmuller group. Tokunaga made study on Zariski κ-plets with Artal Bartolo of Universidad Zaragoza, and gave a new example. This result is in press. Oka intesively studied plane sextic cures. Shimada classified all possible configurations of rational double points on super singular K3 surfaces with Picard number 21.