## 代数幾何学セミナー

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 權業 善範・中村 勇哉・田中公

### 2008年11月07日(金)

16:30-18:00   数理科学研究科棟(駒場) 118号室
Misha Verbitsky 氏 (ITEP and IPMU)
Hyperkaehler SYZ conjecture and stability
[ 講演概要 ]
Let L be a nef bundle on a hyperkaehler manifold. A Hyperkaehler SYZ conjecture postulates that L is semi-ample. As shown by Matsushita, this implies existence of holomorphic Lagrangian fibrations on hyperkaehler manifolds. It was conjectured by many
people, most recently by Tschinkel, Hassett, Huybrechts and Sawon. We prove that a sufficiently big power of L is effective, assuming that L admits a semi-positive metric. A multiplier ideal version of this argument would give effectivity of L^N for any nef L. The proof uses stability and Boucksom's divisorial
Zariski decomposition.