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代数幾何学セミナー
過去の記録 ～06/22｜次回の予定｜今後の予定 06/23～
| 開催情報 | 金曜日 13:30～15:00 数理科学研究科棟(駒場) 118号室 |
|---|---|
| 担当者 | 權業 善範、河上 龍郎 、榎園 誠 |
2011年05月30日(月)
16:30-18:00 数理科学研究科棟(駒場) 126号室
Jungkai Alfred Chen 氏 (National Taiwan University and RIMS)
Kodaira Dimension of Irregular Varieties (ENGLISH)
Jungkai Alfred Chen 氏 (National Taiwan University and RIMS)
Kodaira Dimension of Irregular Varieties (ENGLISH)
[ 講演概要 ]
f:XtoY be an algebraic fiber space with generic geometric fiber F, dimX=n and dimY=m. Then Iitaka's Cn,m conjecture states kappa(X)geqkappa(Y)+kappa(F). In particular, if X is a variety with kappa(X)=0 and f:XtoY is the Albanese map, then Ueno conjecture that kappa(F)=0. One can regard Ueno’s conjecture an important test case of Iitaka’s conjecture in general.
These conjectures are of fundamental importance in the classification of higher dimensional complex projective varieties. In a recent joint work with Hacon, we are able to prove Ueno’s conjecture and Cn,m conjecture holds when Y is of maximal Albanese dimension. In this talk, we will introduce some relative results and briefly sketch the proof.
f:XtoY be an algebraic fiber space with generic geometric fiber F, dimX=n and dimY=m. Then Iitaka's Cn,m conjecture states kappa(X)geqkappa(Y)+kappa(F). In particular, if X is a variety with kappa(X)=0 and f:XtoY is the Albanese map, then Ueno conjecture that kappa(F)=0. One can regard Ueno’s conjecture an important test case of Iitaka’s conjecture in general.
These conjectures are of fundamental importance in the classification of higher dimensional complex projective varieties. In a recent joint work with Hacon, we are able to prove Ueno’s conjecture and Cn,m conjecture holds when Y is of maximal Albanese dimension. In this talk, we will introduce some relative results and briefly sketch the proof.
