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：这个项目主要由德永、三宅和土桥完成。德永主要研究二维通用伽罗瓦盖。两篇关于二维通用伽罗瓦盖和有理椭圆曲面的论文正在出版中。他还证明了二维通用伽罗瓦盖的研究可以简化为有限群的Cremona表示的研究。关于这个问题的文件目前正在编写中。土桥用环几何构造了二面体群和对称群的泛伽罗瓦盖。他还研究了P^2的伽罗瓦覆盖，其普遍覆盖是多盘。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场有关，并给出了显式的简短形式，即所谓的“莫德尔公式”。开放代数变异和奇点的拓扑：Nakamura对Grothendieck-Teichmuller群的研究。德永与萨拉戈萨大学的Artal Bartolo对Zariski - ki -plets进行了研究，并给出了一个新的例子。这一结果已发表。奥卡深入研究了平面性疗法。Shimada分类了Picard数为21的超奇异K3曲面上所有可能的有理双点构型。

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.