  In these notes, we consider self-maps of degree > 1 on a weak del Pezzo
surface X of degree < 8. We show that there are exactly 12 such X, modulo
isomorphism. In particular, K_X^2 > 2, and if X has one self-map of degree > 1
then for every positive integer d there is a self-map of degree d^2 on X. We
prove the Sato conjecture in the present case, the general case of which has
been proved by N. Nakayama.

Algebraic Geometry