Real structures on rational surfaces and automorphisms acting trivially on Picard groups

摘要

In this article, we prove that any complex smooth rational surface X which has no automorphism of positive entropy has a finite number of real forms (this is especially the case if X cannot be obtained by blowing up at points). In particular, we prove that the group of complex automorphisms of X which act trivially on the Picard group of X is a linear algebraic group defined over .