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 $f:X\to Y$, 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.