Maps onto certain Fano threefolds

Abstract

We prove that if X is a smooth projective threefold with b_2=1 and Y is a Fano threefold with b_2=1 , then for a non-constant map f:X\rightarrow Y , the degree of f is bounded in terms of the discrete invariants of X and Y . Also, we obtain some stronger restrictions on maps between certain Fano threefolds.