Duke Mathematical Journal

A surface with discrete and nonfinitely generated automorphism group

Tien-Cuong Dinh and Keiji Oguiso

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Abstract

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

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

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

Permanent link to this document
https://projecteuclid.org/euclid.dmj/1552615313

Digital Object Identifier
doi:10.1215/00127094-2018-0054

Mathematical Reviews number (MathSciNet)
MR3934593

Zentralblatt MATH identifier
07055220

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

Keywords
discrete nonfinitely generated automorphism group infinitely many real forms

Citation

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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