Number Theory Seminar
Joey Lee
UIC
Weak Northcott property and the D-ratio for rational maps
Abstract: In 1950, Northcott proved the height inequality for
morphisms on projective spaces. Let $f:P^n\to P^n$ be a morphism. Then,
there is a constant $C$ depending on the given morphism such that the
height function $h$ satisfies
$h(f(P)) + C > \deg f \, h(P) > h(f(P)) - C$
for all points $P \in P^n$.
Unfortunately, the upper bound of the inequality does not hold
for rational maps. However, we can find weaker inequality by 1)
restricting points on an affine open set and 2) enlarging the upper
bound a little bit. In this talk, I will introduce the D-ratio for
a rational map on projective space and prove the Weak Northcott
property for rational maps.
This seminar is joint with Geometry/Topology/Dynamics.
Wednesday September 8, 2010 at 3:00 PM in SEO 612