Many-sided researches on rationally connected projective varieties-Fano varieties are unirational ?

《科学研究的目标是研究与它们有关的、与它们相关的、和开发主题的、研究结果》。以下结果被发现为理性曲线家族：当一个预测变量X包含一个示例分支：其中一个纤维结构的一般纤维是一条预测线，而A的纤维结构扩展到X。这一年，X继承了A的Bling-Down的财产。更进一步，它有一个应用程序来构建混凝土最小模型。（标题：Lefschetz关于${bf P}^1$-光纤空间和阻塞的超平面部分原则）。我们研究了一个结构的无限序列的结构，一个相互关联的变体。这些变体与非理性、非理性和非理性的变体密切相关。我们特别地用皮卡德第2号确定了这样的变体的结构“标题：关于平滑投影变体的塔理论”。我们现在正在研究立方体3-文件的出生组和四重奏3-文件的统一性。I had a talk on the beManagement of rational curves on inite dimManagement al projective variManagement in 2003 at Kochi Univ.2.Meeting： We organized a meeting for algebraic geometry“higher dimManagement al variManagement”at Kyushu Univ in 2003 and published the report.3。Takagi（在Kyoto Univ的Rims）举办了关于3-dimensional Q-初级风扇变异的讲座，并与我们和Nakayama就变异的endmorphisms进行了讨论。Abe and Aoki （Kyoto Univ） had discussions about the constructions of vector bundles and algebraic stacks respectively.4.An investigator Takayama published "Iitaka fibrations via multiplier ideals"， Furushima "non-normal Del Pesso surfaces" compactiification of $C^3$" and Hanamura "relative Chow-Kuneth projectors for modular variManagement " and so on respectively。

The aim of the scientific research is to study rationally connected projective varieties and problems related with them and to develope them.1.Reseach results.・The following results were obtained as for families of rational curves : When a projective variety X contains an ample divisor A which has fiber structure whose general fiber is a projective line, the fiber structure of A is extended to X. This yields that X inherits the property of blowing-down from A. Furthermore it has an application to the procedure for constructing conclete minimal model.(Title : Hyperplane section principle of Lefschetz about ${bf P}^1$-fiber space and blowing-down).・We studied the structure of infinite sequence of rationally connected varieties. These varieties are closely related with unirational, toric and abelian varieties. Particularly we determined the structure of such varieties with Picard number 2 「Title : Tower theorem on smooth projective varieties」。・We are now studying the birational group of cubic 3-folds and the unirationality of quartic 3-folds.・I had a talk on the behavior of rational curves on infinite dimensional projective varieties in 2003 at Kochi Univ.2.Meeting: We organized a meeting for algebraic geometry "higher dimensional varieties" at Kyushu Univ in 2003 and published the report.3.Discussions. Takagi(in Rims of Kyoto Univ) had lectures of 3-dimensional Q-primary Fano varieties -and discussion with us and Nakayama did the one on endmorphisms of varieties. Abe and Aoki (Kyoto Univ) had discussions about the constructions of vector bundles and algebraic stacks respectively.4.An investigator Takayama published "Iitaka fibrations via multiplier ideals", Furushima "non-normal Del Pesso surfaces" "compactification of $C^3$" and Hanamura "relative Chow-Kuneth projectors for modular varieties" and so on respectively.