Seminar on Complex Analysis and Complex Geometry - Fall 2023

On Wednesday when no extramural speaker is listed, the members of the complex geometry group may meet for a working seminar. For more information, send an email to Gordon Heier.

Wednesday, November 29, 2023, 11am-12noon, S 101 (note the special room)

Title: A Schmidt-Nochka Theorem for closed subschemes

Speaker: Aaron Levin, Michigan State University

Abstract: Schmidt's Subspace Theorem and Cartan's Second Main Theorem occupy central roles in Diophantine approximation and Nevanlinna theory, respectively. Proving a conjecture of Cartan, Nochka extended the Second Main Theorem to hyperplanes in so-called m-subgeneral position, and Ru and Wong proved an analogous extension of Schmidt's theorem. I will discuss recent work with Gordon Heier proving an inequality which melds inequalities of Schmidt and Nochka in the general setting of closed subschemes, and in particular gives a partial solution to generalizing the results of Nochka and Ru-Wong to hypersurfaces in projective space.