K3 Lehmer映射的方程

IF 0.9 1区数学 Q2 MATHEMATICS

Journal of Algebraic Geometry Pub Date : 2021-03-28 DOI:10.1090/jag/810

Simon Brandhorst, N. Elkies

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引用次数: 3

摘要

C.T.McMullen用Lehmer数的对数给出的熵的自同构证明了K3曲面的存在，该自同构是复曲面的自同构中可能的最小值。我们从McMullen提供的Hodge理论模型重建了曲面及其自同构的方程组。该方法是计算机辅助的，并依赖于有限的非辛自同构、p p-adic提升、椭圆fibration和Z\mathbb｛Z｝-格的Kneer邻居方法。它可以应用于从椭圆K3曲面在Neron Severi格上的作用重建其任何自同构。

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Equations for a K3 Lehmer map

C. T. McMullen proved the existence of a K3 surface with an automorphism of entropy given by the logarithm of Lehmer’s number, which is the minimum possible among automorphisms of complex surfaces. We reconstruct equations for the surface and its automorphism from the Hodge theoretic model provided by McMullen. The approach is computer aided and relies on finite non-symplectic automorphisms, p p -adic lifting, elliptic fibrations and the Kneser neighbor method for Z \mathbb {Z} -lattices. It can be applied to reconstruct any automorphism of an elliptic K3 surface from its action on the Neron-Severi lattice.

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来源期刊

Journal of Algebraic Geometry 数学-数学

CiteScore

2.70

自引率

5.60%

发文量

审稿时长

>12 weeks

期刊介绍： The Journal of Algebraic Geometry is devoted to research articles in algebraic geometry, singularity theory, and related subjects such as number theory, commutative algebra, projective geometry, complex geometry, and geometric topology. This journal, published quarterly with articles electronically published individually before appearing in an issue, is distributed by the American Mathematical Society (AMS). In order to take advantage of some features offered for this journal, users will occasionally be linked to pages on the AMS website.