On geography of arrangements of lines

Giancarlo Urzúa
Universidad Católica de Chile
Abstract:
Let 
\[k\]
be an arbitrary field. An arrangement of lines is a finite collection of lines in the projective plane over 
\[k\]
. I will talk about distribution of Chern invariants of arrangements, which are numerical combinatorial invariants attached to them. The purpose is to present what is known, and to present two open questions in relation to realization of Chern slopes for 
\[k=\mathbb C\]
(complex numbers) and
\[k=\mathbb Q\]
(rational numbers).