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過去の記録 ～04/19｜次回の予定｜今後の予定 04/20～
| 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 |
2014年07月07日(月)
15:30-17:00 数理科学研究科棟(駒場) 122号室
谷本翔 氏 (Rice University)
Balanced line bundles (JAPANESE)
谷本翔 氏 (Rice University)
Balanced line bundles (JAPANESE)
[ 講演概要 ]
A conjecture of Batyrev and Manin relates arithmetic properties of
varieties with big anticanonical class to geometric invariants; in
particular, counting functions defined by metrized ample line bundles
and the corresponding asymptotics of rational points of bounded height
are interpreted in terms of cones of effective divisors and certain
thresholds with respect to these cones. This framework leads to the
notion of balanced line bundles, whose counting functions, conjecturally,
capture generic distributions of rational points. We investigate
balanced line bundles in the context of the Minimal Model Program, with
special regard to the classification of Fano threefolds and Mori fiber
spaces.
This is joint work with Brian Lehmann and Yuri Tschinkel.
A conjecture of Batyrev and Manin relates arithmetic properties of
varieties with big anticanonical class to geometric invariants; in
particular, counting functions defined by metrized ample line bundles
and the corresponding asymptotics of rational points of bounded height
are interpreted in terms of cones of effective divisors and certain
thresholds with respect to these cones. This framework leads to the
notion of balanced line bundles, whose counting functions, conjecturally,
capture generic distributions of rational points. We investigate
balanced line bundles in the context of the Minimal Model Program, with
special regard to the classification of Fano threefolds and Mori fiber
spaces.
This is joint work with Brian Lehmann and Yuri Tschinkel.
