代数幾何学セミナー

過去の記録 ~12/08次回の予定今後の予定 12/09~

開催情報 火曜日 10:30~11:30 or 12:00 数理科学研究科棟(駒場) ハイブリッド開催/002号室
担当者 權業 善範・中村 勇哉・田中公

2022年11月22日(火)

10:30-12:00   数理科学研究科棟(駒場) 002号室
90分ハイブリッド開催です。
谷本祥 氏 (名古屋多元)
Non-free sections of Fano fibrations (日本語)
[ 講演概要 ]
Manin’s Conjecture predicts the asymptotic formula for the counting function of rational points over number fields or global function fields. In the late 80’s, Batyrev developed a heuristic argument for Manin’s Conjecture over global function fields, and the assumptions underlying Batyrev’s heuristics are refined and formulated as Geometric Manin’s Conjecture. Geometric Manin’s Conjecture is a set of conjectures regarding properties of the space of sections of Fano fibrations, and it consists of three conjectures: (i) Pathological components are controlled by Fujita invariants; (ii) For each nef algebraic class, a non-pathological component which should be counted in Manin’s Conjecture is unique (This component is called as Manin components); (iii) Manin components exhibit homological or motivic stability. In this talk we discuss our proofs of GMC (i) over complex numbers using theory of foliations and the minimal model program. Using this result, we prove that these pathological components are coming from a bounded family of accumulating maps. This is joint work in progress with Brian Lehmann and Eric Riedl.