代数幾何学セミナー

過去の記録 ~08/18次回の予定今後の予定 08/19~

開催情報 月曜日 15:30~17:00 数理科学研究科棟(駒場) 122号室
担当者 權業 善範・中村 勇哉・高木 俊輔

2017年06月27日(火)

15:30-17:00   数理科学研究科棟(駒場) 122号室
岸本 崇 氏 (埼玉大学)
Cylinders in del Pezzo fibrations (English )
[ 講演概要 ]
The cylinder is, by definition, an algebraic variety of the form Z × A1 . Certainly it is geometrically a very simple object, but it plays often an important role to connect unipotent group actions on special kinds of affine algebraic varieties to projective geometry. From the point of view of birational geometry, it is essential to look into cylinders found on Mori fiber spaces. In this talk, we shall focus mainly on Mori fiber spaces of relative dimension two or three. One of main results asserts that a del Pezzo fibration π : V → W contains a cylinder respecting the structure of π (so-called a vertical cylinder) if and only if the degree deg π of π is greater than or equal to 5 and π admits a rational section. Especially, in case of dim V = 3, the existence of a vertical cylinder is equivalent to saying deg π ≧ 5 in consideration of Tsen’s theorem, nevertheless, it is worthwhile to note that the affine 3-space A3C is embedded into certains del Pezzo fibrations π : V → P1C of deg π ≦ 4 in a twisted way. This is a joint work with Adrien Dubouloz (Universit ́e de Bourgogne).