Duke Mathematical Journal

A surface with discrete and nonfinitely generated automorphism group

Tien-Cuong Dinh and Keiji Oguiso

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We show that there is a smooth complex projective variety, of any dimension greater than or equal to 2, whose automorphism group is discrete and not finitely generated. Moreover, this variety admits infinitely many real forms which are mutually nonisomorphic over R. Our result is inspired by the work of Lesieutre and answers questions by Dolgachev, Esnault, and Lesieutre.

Article information

Duke Math. J., Volume 168, Number 6 (2019), 941-966.

Received: 14 December 2017
Revised: 18 July 2018
First available in Project Euclid: 15 March 2019

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 14J50: Automorphisms of surfaces and higher-dimensional varieties
Secondary: 14G30 14J28: $K3$ surfaces and Enriques surfaces

discrete nonfinitely generated automorphism group infinitely many real forms


Dinh, Tien-Cuong; Oguiso, Keiji. A surface with discrete and nonfinitely generated automorphism group. Duke Math. J. 168 (2019), no. 6, 941--966. doi:10.1215/00127094-2018-0054. https://projecteuclid.org/euclid.dmj/1552615313

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