关于阶为$21自同构群的假射影平面方程

Pub Date : 2023-05-30 DOI:10.46298/epiga.2023.8507

Lev Borisov

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引用次数: 0

摘要

我们研究了双纤维和三纤维的Dolgachev椭圆曲面，得到了两对新的$21$自同构假投影平面的显式方程，从而完成了这类自同构群假投影平面显式方程的求解任务。这尤其包括J. Keum发现的假投影平面。

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On equations of fake projective planes with automorphism group of order $21$

We study Dolgachev elliptic surfaces with a double and a triple fiber and find explicit equations of two new pairs of fake projective plane with $21$ automorphisms, thus finishing the task of finding explicit equations of fake projective planes with this automorphism group. This includes, in particular, the fake projective plane discovered by J. Keum.

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