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Seminar on Geometric Complex Analysis
Seminar information archive ～01/24｜Next seminar｜Future seminars 01/25～
| Date, time & place | Monday 10:30 - 12:00 128Room #128 (Graduate School of Math. Sci. Bldg.) |
|---|---|
| Organizer(s) | Kengo Hirachi, Shigeharu Takayama |
2017/04/17
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Yuta Kusakabe (Osaka University)
Dense holomorphic curves in spaces of holomorphic maps
Yuta Kusakabe (Osaka University)
Dense holomorphic curves in spaces of holomorphic maps
[ Abstract ]
We study when there exists a dense holomorphic curve in a space of holomorphic maps from a Stein space. Our results state that for any bounded convex domain $\Omega \Subset \mathbb{C}^n$ and any connected complex manifold $Y$, the space $\mathcal{O}(\Omega,Y)$ contains a dense holomorphic disc, and that $Y$ is an Oka manifold if and only if for any Stein space $X$ there exists a dense entire curve in every path component of $\mathcal{O}(X,Y)$. The latter gives a new characterization of Oka manifolds. As an application of the former, we construct universal maps from bounded convex domains to any connected complex manifold.
We study when there exists a dense holomorphic curve in a space of holomorphic maps from a Stein space. Our results state that for any bounded convex domain $\Omega \Subset \mathbb{C}^n$ and any connected complex manifold $Y$, the space $\mathcal{O}(\Omega,Y)$ contains a dense holomorphic disc, and that $Y$ is an Oka manifold if and only if for any Stein space $X$ there exists a dense entire curve in every path component of $\mathcal{O}(X,Y)$. The latter gives a new characterization of Oka manifolds. As an application of the former, we construct universal maps from bounded convex domains to any connected complex manifold.
