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arXiv · 2609.40045

A rational surface with discrete and non-finitely generated automorphism group

Tien-Cuong Dinh·Keiji Oguiso·Xun Yu·Qi Zhou
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Abstract

We construct a smooth complex projective rational surface whose automorphism group is discrete and not finitely generated. It is obtained by blowing up a point on a branch curve of a rational quotient of a product Kummer surface. Every point with transcendental coordinate gives such a surface. The proof uses leading jets along the branch curve, the complete family of blowups and the cubic intersection of the family, which are not being considered in relevant earlier works.

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Tien-Cuong Dinh, Keiji Oguiso, Xun Yu, Qi Zhou. 2026-09-30. A rational surface with discrete and non-finitely generated automorphism group. https://arxiv.org/abs/2609.40045

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