Speaker: Norifumi Ojiro (Hiroshima)

Title: Rational curves on a smooth Hermitian surface

Abstract:
We study the set R of nonplanar rational curves of degree d<q+2 on a smooth Hermitian 
surface X of degree q+1 defined over an algebraically closed field of characteristic 
p>0, where q is a power of p. We prove that R is the empty set when d<q+1. 
In the case where d=q+1, we count the number of elements of R by showing that 
the group of projective automorphisms of X acts transitively on R and by determining 
the stabilizer subgroup. In the special case where X is the Fermat surface, we present 
an element of R explicitly.