Real structures on rational surfaces and automorphisms acting trivially on Picard groups
Real structures on rational surfaces and automorphisms acting trivially on Picard groups
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有理曲面上的实结构和作用在皮卡德群上的自同构
DOI：
10.1007/s00209-015-1581-x
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发表时间：
2014
影响因子：
0.8
通讯作者：
Mohamed Benzerga
中科院分区：
文献类型：
--
作者：
Mohamed Benzerga
本文证明了任何不具有正熵自同构的复光滑有理曲面X都有有限个真实的形式（特别是当X不能通过点爆破得到时）。特别地，我们证明了X的复自同构群平凡地作用在X的Picard群上是定义在上的线性代数群。
In this article, we prove that any complex smooth rational surfaceXwhich has no automorphism of positive entropy has a finite number of real forms (this is especially the case ifXcannot be obtained by blowing upatpoints). In particular, we prove that the groupof complex automorphisms ofXwhich act trivially on the Picard group ofXis a linear algebraic group defined over.