[geometry-ml:04082] Geometric Complex Analysis Seminar 6/29

[Kengo Hirachi]

皆様

複素解析幾何セミナー@東大数理のご案内です。

2020年06月29日(月)
10:30-12:00    Zoom 開催
日下部佑太 氏 (大阪大学)
Oka properties of complements of holomorphically convex sets

[ 講演概要 ]
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 
C
n
C
n
 
(
n
>
1
)
(
n
>
1
)
 is Oka. The relative version of the main theorem can also be proved. As an application, we show that the complement 
C
n
∖
R
k
C
n
∖
R
k
 of a totally real affine subspace is Oka if 
n
>
1
n
>
1
 and 
(
n
,
k
)
≠
(
2
,
1
)
,
(
2
,
2
)
,
(
3
,
3
)
(
n
,
k
)
≠
(
2
,
1
)
,
(
2
,
2
)
,
(
3
,
3
)
.

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世話人
平地 健吾, 高山 茂晴
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