Speaker : Yoichi Miyaoka(The University of Tokyo)
Title : On the canonical degree of curves on a surface
Time : 2012-11-22 (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 .