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On Endomorphisms of Algebraic Surfaces

D. -Q. Zhang
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Abstract

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.

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D. -Q. Zhang. 2002-10-02. On Endomorphisms of Algebraic Surfaces. https://arxiv.org/abs/math/0210021

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