## Duke Mathematical Journal

### A surface with discrete and nonfinitely generated automorphism group

#### 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 $\mathbb{R}$. 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
Revised: 18 July 2018
First available in Project Euclid: 15 March 2019

https://projecteuclid.org/euclid.dmj/1552615313

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

Mathematical Reviews number (MathSciNet)
MR3934593

Zentralblatt MATH identifier
07055220

#### 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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