论文标题
具有无限多种真实形式的光滑投射表面
Smooth projective surfaces with infinitely many real forms
论文作者
论文摘要
本文的目的是双重的。首先，我们证实了给定平滑复杂的投影品种的实际形式有限的一些基本标准，该标准就自动形态群体的离散部分的Galois共同体，锥形构象和拓扑熵而言。然后，我们将它们应用它们表明，除非它是理性的或非最小的表面，否则最多有许多非同态真实形式有限的复杂的射斑表面表面有限。在本文的第二部分中，我们构建了一个富集表面，其爆炸在某一时刻接受了无限的许多非同构真实形式。这向我们回答了Kondo的问题，还表明了三种特殊情况确实发生了。
The aim of this paper is twofold. First of all, we confirm a few basic criteria of the finiteness of real forms of a given smooth complex projective variety, in terms of the Galois cohomology set of the discrete part of the automorphism group, the cone conjecture and the topological entropy. We then apply them to show that a smooth complex projective surface has at most finitely many non-isomorphic real forms unless it is either rational or a non-minimal surface birational to either a K3 surface or an Enriques surface. In the second part of the paper, we construct an Enriques surface whose blow-up at one point admits infinitely many non-isomorphic real forms. This answers a question of Kondo to us and also shows the three exceptional cases really occur.
