The Cayley-Oguiso automorphism of positive entropy on a K3 surface
The Cayley-Oguiso automorphism of positive entropy on a K3 surface
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K3 面上正熵的 Cayley-Oguiso 自同构
DOI：
10.3934/jmd.2013.7.75
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发表时间：
2012
期刊：
影响因子：
--
通讯作者：
R. Luijk
中科院分区：
文献类型：
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作者：
Dino Festi;Alice Garbagnati;B. Geemen;R. Luijk
最近Oguiso表明存在的K3表面承认一个不动点自由自同构的正熵。Oguiso使用的K3曲面具有特定的秩2 Picard晶格。我们表明，使用Beauville的结果，这些表面因此是行列式四次曲面。很久以前，凯莱构造了这种行列式曲面的自同构。我们表明，凯莱的自同构与Oguiso的自由自同构相吻合。我们还展示了一个明确的例子，行列式四次的皮卡德格有确切的秩2，因此，我们有一个明确的描述的自同构。
Recently Oguiso showed the existence of K3 surfaces that admit a fixed point free automorphism of positive entropy. The K3 surfaces used by Oguiso have a particular rank two Picard lattice. We show, using results of Beauville, that these surfaces are therefore determinantal quartic surfaces. Long ago, Cayley constructed an automorphism of such determinantal surfaces. We show that Cayley's automorphism coincides with Oguiso's free automorphism. We also exhibit an explicit example of a determinantal quartic whose Picard lattice has exactly rank two and for which we thus have an explicit description of the automorphism.