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Seminar on Geometric Complex Analysis
Seminar information archive ～05/21｜Next seminar｜Future seminars 05/22～
| Date, time & place | Monday 10:30 - 12:00 128Room #128 (Graduate School of Math. Sci. Bldg.) |
|---|---|
| Organizer(s) | Kengo Hirachi, Shigeharu Takayama |
2020/06/29
10:30-12:00 Online
KUSAKABE Yuta (Osaka University)
Oka properties of complements of holomorphically convex sets
https://forms.gle/vSFPoVR6ugrkTGhX7
KUSAKABE Yuta (Osaka University)
Oka properties of complements of holomorphically convex sets
[ Abstract ]
A complex manifold is called an Oka manifold if the Oka principle for maps from Stein spaces holds. In this talk, we consider the question of when a holomorphically convex set in an Oka manifold has an Oka complement. Our main theorem states that the complement of a compact holomorphically convex set in a Stein manifold with the density property is an Oka manifold.
This gives a positive answer to the well-known long-standing problem in Oka theory whether the complement of a compact polynomially convex set in Cn (n>1) is Oka. The relative version of the main theorem can also be proved.
As an application, we show that the complement Cn∖Rk of a totally real affine subspace is Oka if n>1 and (n,k)≠(2,1),(2,2),(3,3).
[ Reference URL ]A complex manifold is called an Oka manifold if the Oka principle for maps from Stein spaces holds. In this talk, we consider the question of when a holomorphically convex set in an Oka manifold has an Oka complement. Our main theorem states that the complement of a compact holomorphically convex set in a Stein manifold with the density property is an Oka manifold.
This gives a positive answer to the well-known long-standing problem in Oka theory whether the complement of a compact polynomially convex set in Cn (n>1) is Oka. The relative version of the main theorem can also be proved.
As an application, we show that the complement Cn∖Rk of a totally real affine subspace is Oka if n>1 and (n,k)≠(2,1),(2,2),(3,3).
https://forms.gle/vSFPoVR6ugrkTGhX7
