Birational automorphisms of quartic Hessian surfaces
Birational automorphisms of quartic Hessian surfaces
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四次 Hessian 曲面的双有理自同构
DOI：
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发表时间：
2001
期刊：
影响因子：
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通讯作者：
J. Keum
中科院分区：
文献类型：
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作者：
I. Dolgachev;J. Keum
我们找到了一般三次曲面的黑森曲面的双态自同构群的生成元。它的非奇异极小模型是一个具有16阶Picard格的K3曲面，它自然地嵌入到26阶签名(1，25)的偶么模格II 1，25中。生成器与相对于某些水蛭根的反射有关。在近藤的工作中，类似的观察首先出现在四次Kummer曲面的情况下。我们将解释我们的生成元如何与一般四次Kummer曲面的双态自同构群的生成元有关，该四次Kummer曲面在双态同构于特殊的Hessian曲面。
We find generators of the group of birational automorphisms of the Hessian surface of a general cubic surface. Its nonsingular minimal model is a K3 surface with the Picard lattice of rank 16 which embeds naturally in the even unimodular lattice II 1,25 of rank 26 and signature (1,25). The generators are related to reflections with respect to some Leech roots. A similar observation was made first in the case of quartic Kummer surfaces in the work of Kondo. We shall explain how our generators are related to the generators of the group of birational automorphisms of a general quartic Kummer surface which is birationally isomorphic to a special Hessian surface.