代数幾何学セミナー
過去の記録 ~05/02|次回の予定|今後の予定 05/03~
開催情報 | 金曜日 13:30~15:00 数理科学研究科棟(駒場) 118号室 |
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担当者 | 權業 善範、河上 龍郎 、榎園 誠 |
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
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.
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.