Speaker :
 Yoichi Miyaoka(The University of Tokyo) 

Title :

On the canonical degree of curves on a surface 
Time :
 20121122 (Thu) 16:15  17:15 
Place : 
Lecture Hall, Inst. of Mathematics 

Abstract: 
A conjecture of Lang predicts that a variety of general type
contains a proper closed
algebraic subset such that all the rational curves and elliptic
curves on are
necessarily contained in .
Though Kodaira proved a weaker result to the effect that
the union of all the rational/elliptic curves on has Lebesgue
measure zero,
the conjecture is still wide open, even in the case where is a surface.
We discuss this problem and prove that, if satisfies a certain
topological condition, we can effectively bound the number of
rational/elliptic curves
on . 
