On Endomorphisms of Algebraic Surfaces
代数几何
2018-06-20 v1
摘要
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.
引用
@article{arxiv.math/0210021,
title = {On Endomorphisms of Algebraic Surfaces},
author = {D. -Q. Zhang},
journal= {arXiv preprint arXiv:math/0210021},
year = {2018}
}
备注
15 pages, Contemporary Math. Amer. Math. Soc. to appear