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Seminar on Geometric Complex Analysis
Seminar information archive ～04/19｜Next seminar｜Future seminars 04/20～
| Date, time & place | Monday 10:30 - 12:00 128Room #128 (Graduate School of Math. Sci. Bldg.) |
|---|---|
| Organizer(s) | Kengo Hirachi, Shigeharu Takayama |
2018/10/29
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Shin-ichi Matsumura (Tohoku University)
On morphisms of compact Kaehler manifolds with semi-positive holomorphic sectional curvature (JAPANESE)
Shin-ichi Matsumura (Tohoku University)
On morphisms of compact Kaehler manifolds with semi-positive holomorphic sectional curvature (JAPANESE)
[ Abstract ]
In this talk, we consider a smooth projective variety $X$ with semi-positive holomorphic "sectional" curvature, motivated by generalizing Howard-Smyth-Wu's structure theorem and Mok's result for compact Kaehler manifold with semi-positive "bisectional" curvature.
We prove that, if $X$ admits a holomorphic maximally rationally connected fibration $X ¥to Y$, then the morphism is always smooth (that is, a submersion), that the image $Y$ admits a finite ¥'etale cover $T ¥to Y$ by a complex
torus $T$, and further that all the fibers $F$ are isomorphic.
This gives a structure theorem for $X$ when $X$ is a surface.
Moreover we show that $X$ is rationally connected, if the holomorphic sectional curvature is quasi-positive.
This result gives a generalization of Yau's conjecture.
In this talk, we consider a smooth projective variety $X$ with semi-positive holomorphic "sectional" curvature, motivated by generalizing Howard-Smyth-Wu's structure theorem and Mok's result for compact Kaehler manifold with semi-positive "bisectional" curvature.
We prove that, if $X$ admits a holomorphic maximally rationally connected fibration $X ¥to Y$, then the morphism is always smooth (that is, a submersion), that the image $Y$ admits a finite ¥'etale cover $T ¥to Y$ by a complex
torus $T$, and further that all the fibers $F$ are isomorphic.
This gives a structure theorem for $X$ when $X$ is a surface.
Moreover we show that $X$ is rationally connected, if the holomorphic sectional curvature is quasi-positive.
This result gives a generalization of Yau's conjecture.
