Synthetic research of algebraic geometry with an expectation of wide applications

石田研究风扇定义复曲面品种。他把它们描述为基于半群的方案。中村对简单奇点的麦凯对应作了解释。他构造了一个自然紧化的模空间的交换品种。Shioda研究了椭圆曲线的Mordell-Weil格和Jacobian簇，Mori给出了半-Weil格存在定理的直接证明，Shioda研究了椭圆曲线的Mordell-Weil格和Jacobian簇，Mori给出了半-Weil格存在定理的直接证明。超曲面孤立奇点的泛变形空间，得到了有理椭圆曲面中高亏格曲线的计数公式证明了由有理曲线张成的具有某些特殊性质的射影簇是射影空间或二次超曲面，Hashimoto研究了具有仿射群作用的仿射格式。其他研究者和合作者组织了代数专题讨论会、代数几何专题讨论会和交换代数专题讨论会。我们通过这些研讨会获得的结果发表在这些研讨会的会议记录中。

Ishida studied on fans which define toric varieties. He described them as schemes based on semigroups.Nakamura gave an explanation on the McKay correspondences of simple singularities. And he constructed a natural compactification of the moduli space of abelian varieties.Katsura worked on the code theory. He also got some results on hights of the formal Brauer groups defined for polarized K3 surfaces in positive characteristics.Shioda studied on the Mordell-Weil lattices of elliptic curves and Jacobian varieties.Mori gave a direct proof of the existing theorem of the semi-universal deformation space of hypersurface isolated singularities.Saito got a formula for the enumeration problem of the curves with high genera embedded in rational elliptic surfaces.Sato proved that projective varieties with some special properties spanned by rational curves is either a projective space or a quadric hypersurface.Hashimoto studied on affine schemes with actions of affine group schemes. And he applied the results for the invariant theory.Other investigators and cooperators organized The Symposium of Algebra, The Symposium of Algebraic geometry and The Symposium of Commutative Algebras. The results which we got through these symposia are published in the proceedings of these symposia.