Seminar in Real and Complex Geometry

Monday, May 25, 2020, 16:00-18:00, online (via zoom)

Boulos El Hilany
(Johannes Radon Institute for Computational and Applied Mathematics, Linz)

Counting isolated points outside the image of a polynomial map


A dominant polynomial map from the complex plane to itself gives rise to a finite set of curves and isolated points outside its image. Z. Jelonek provided an upper bound on the number of such isolated points that is quadratic in, and depends only on, the degrees of the polynomials involved. I will introduce in this talk a large family of dominant non-proper maps above for which this upper bound is linear in the degrees. Moreover, I will illustrate constructions proving asymptotical sharpness up to multiplication by a constant.