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代数幾何学セミナー
過去の記録 ～04/05｜次回の予定｜今後の予定 04/06～
| 開催情報 | 金曜日 13:30～15:00 数理科学研究科棟(駒場) ハイブリッド開催/117号室 |
|---|---|
| 担当者 | 權業 善範、中村 勇哉、田中 公 |
2010年07月05日(月)
16:40-18:10 数理科学研究科棟(駒場) 126号室
古川 勝久 氏 (早稲田大学)
Rational curves on hypersurfaces (JAPANESE)
古川 勝久 氏 (早稲田大学)
Rational curves on hypersurfaces (JAPANESE)
[ 講演概要 ]
Our purpose is to study the family of smooth rational curves of degree e lying on a hypersurface of degree d in mathbbPn, and to investigate properties of this family (e.g., dimension, smoothness, connectedness).
Our starting point is the research about the family of lines (i.e., e=1), which was studied by W. Barth and A. Van de Ven over mathbbC, and by J. Koll\\'{a}r over an algebraically closed field of arbitrary characteristic.
For the degree e>1, the family of rational curves was studied by J. Harris, M. Roth, and J. Starr over mathbbC in the case of d<(n+1)/2.
In this talk, we study the family of rational curves in arbitrary characteristic under the assumption e=2,3 and d>1, or e>3 and d>2e−4.
Our purpose is to study the family of smooth rational curves of degree e lying on a hypersurface of degree d in mathbbPn, and to investigate properties of this family (e.g., dimension, smoothness, connectedness).
Our starting point is the research about the family of lines (i.e., e=1), which was studied by W. Barth and A. Van de Ven over mathbbC, and by J. Koll\\'{a}r over an algebraically closed field of arbitrary characteristic.
For the degree e>1, the family of rational curves was studied by J. Harris, M. Roth, and J. Starr over mathbbC in the case of d<(n+1)/2.
In this talk, we study the family of rational curves in arbitrary characteristic under the assumption e=2,3 and d>1, or e>3 and d>2e−4.
