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Seminar on Geometric Complex Analysis
Seminar information archive ～05/01｜Next seminar｜Future seminars 05/02～
| Date, time & place | Monday 10:30 - 12:00 128Room #128 (Graduate School of Math. Sci. Bldg.) |
|---|---|
| Organizer(s) | Kengo Hirachi, Shigeharu Takayama |
2011/11/07
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Junjiro Nocuchi (University of Tokyo)
Oka's extra-zero problem and related topics (JAPANESE)
Junjiro Nocuchi (University of Tokyo)
Oka's extra-zero problem and related topics (JAPANESE)
[ Abstract ]
The main part of this talk is a joint work with my colleagues, M. Abe and S. Hamano. After the solution of Cousin II problem by K. Oka III in 1939, he thought an extra-zero problem in 1945 (his posthumous paper) asking if it is possible to solve an arbitrarily given Cousin II problem adding some extra-zeros whose support is disjoint from the given one. Some special case was affirmatively confirmed in dimension two and a counter-example in dimension three or more was obtained. We will give a complete solution of this problem with examples and to discuss some new questions. An example on a toric variety of which idea is based on K. Stein's paper in 1941 has some special interest and will be discussed. I would like also to discuss some analytic intersections form the viewpoint of Nevanlinna theory.
The main part of this talk is a joint work with my colleagues, M. Abe and S. Hamano. After the solution of Cousin II problem by K. Oka III in 1939, he thought an extra-zero problem in 1945 (his posthumous paper) asking if it is possible to solve an arbitrarily given Cousin II problem adding some extra-zeros whose support is disjoint from the given one. Some special case was affirmatively confirmed in dimension two and a counter-example in dimension three or more was obtained. We will give a complete solution of this problem with examples and to discuss some new questions. An example on a toric variety of which idea is based on K. Stein's paper in 1941 has some special interest and will be discussed. I would like also to discuss some analytic intersections form the viewpoint of Nevanlinna theory.
