An effective Schottky-Landau theorem for holomorphic curves in projective space; WILLIAM CHERRY (UNT)

Event Information
Category:
RTG Logic and Dynamics Seminar
Event Date:
12-12-2011 1:30 AM
Event Location:
GAB 461

Speaker: WILLIAM CHERRY (University of North Texas)

Title: An effective Schottky-Landau theorem for holomorphic curves in projective space

Abstract: In 1944, Dufresnoy published a generalization of Landau's theorem: if a holomorphic map from the unit disc to complex projective n-space omits 2n+1 hyperplanes in general position, then the Fubini-Study derivative of the map at the origin is bounded above by a constant. Dufresnoy's argument, making use of a normal families argument, does not effectively estimate the constant, and Dufresnoy commented that from his argument, the constant depends in an "unkown way" on the omitted hyperplanes. I will discuss joint work with Alex Eremenko about how the potential theoretic method of Eremenko and Sodin can be used to give an effective estimate for Dufresnoy's constant which, although non-sharp, gives a good sense of how Dufresnoy's constant depends on the geometry of the configuration of the omitted hyperplanes and has almost the best possible asymptotic behavior as the hyperplanes degenerate away from general position.