- Title: Polynomial convexity for
unbounded closed sets in C^n - Speaker: Dr. Thomas Pawlaschyk (Universität Wuppertal) - Abstract: I will introduce different
types of polynomially convex hulls for arbitrary closed sets A in C^n. I will give some of their
properties and examples. One of these hulls is the closure of the union of the
polynomially convex hulls of all compact sets lying inside A. Another one is the collection of
points which satisfy the following property: if there is a non-negative
continuous entire plurisubharmonic function which vanishes on A, then it already vanishes at this
point.
These definitions arise naturally from the
characterization of polynomially convex hulls in the compact case. In fact, in
contrary to the compact case, it seems that they are not the same. To see this,
I will give an example in C^2. At the end, I will explain
the situation in $\cbb$ and discuss our recent observations on unbounded hulls.
The study of these hulls is a joint work with T. Harz and Y. Nagata. - Place: GAIA Seminar Room (#106, Math Science bldg.) |
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