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| 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 |
2013年11月25日(月)
15:30-17:00 数理科学研究科棟(駒場) 122号室
小池 貴之 氏 (東大数理)
Minimal singular metrics of some line bundles with infinitely generated section rings (JAPANESE)
小池 貴之 氏 (東大数理)
Minimal singular metrics of some line bundles with infinitely generated section rings (JAPANESE)
[ 講演概要 ]
We consider Hermitian metrics of pseudo-effective line bundles on smooth
projective varieties defined over $\\mathbb{C}$.
Especially we are interested in (possibly singular) Hermitian metrics
with semi-positive curvatures when the section rings are not finitely generated.
We study where and how minimal singular metrics, special Hermitian
metrics with semi-positive curvatures, diverges in the following two situations;
a line bundle admitting no Zariski decomposition even after any
modifications (Nakayama example)
and a nef line bundle $L$ on $X$ satisfying $D \\subset |mL|$ and $|mL-D|
= \\emptyset$ for some divisor $D \\subset X$ and for all $m \\geq 1$ (
Zariski example).
We consider Hermitian metrics of pseudo-effective line bundles on smooth
projective varieties defined over $\\mathbb{C}$.
Especially we are interested in (possibly singular) Hermitian metrics
with semi-positive curvatures when the section rings are not finitely generated.
We study where and how minimal singular metrics, special Hermitian
metrics with semi-positive curvatures, diverges in the following two situations;
a line bundle admitting no Zariski decomposition even after any
modifications (Nakayama example)
and a nef line bundle $L$ on $X$ satisfying $D \\subset |mL|$ and $|mL-D|
= \\emptyset$ for some divisor $D \\subset X$ and for all $m \\geq 1$ (
Zariski example).
