1999 Fiscal Year Final Research Report Summary
Synthetic research of algebraic geometry with an expectation of wide applications
| Project/Area Number |
09304001
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| Research Category |
Grant-in-Aid for Scientific Research (A)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Algebra
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| Research Institution | TOHOKU UNIVERSITY |
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Principal Investigator |
ISHIDA Masanori Mathematical Institute, Tohoku University, professor, 大学院・理学研究科, 教授 (30124548)
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| Co-Investigator(Kenkyū-buntansha) |
KATSURA Toshiyuki Department of Mathematical Sciences, University of Tokyo, professor, 大学院・数理科学研究科, 教授 (40108444)
NAKAMURA Iku Department of Mathematics, Hokkaido University, professor, 大学院・理学研究科, 教授 (50022687)
ODA Tadao Mathematical Institute, Tohoku University, professor, 大学院・理学研究科, 教授 (60022555)
HASHIMOTO Mitsuyasu Department of Mathematics, Nagoya University, associate professor, 大学院・多元数理科学研究科, 助教授 (10208465)
SATO Eiichi Department of Mathematical Sciences, Kyushu University, professor, 大学院・数理学研究科, 教授 (10112278)
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| Project Period (FY) |
1997 – 1999
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| Keywords | Algebraic geometry / Algebraic variety / Toric variety / Commutative algebra / Computational geometry / Abelian variety |
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| Research Abstract |
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.
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