The Nieto quintic is Janus-like
type: Item
instance of: scholarly article
title: The Nieto quintic is Janus-like
zbMATH Open document ID: 0956.14032
author: Bruce Hunt
published in: Journal of Differential Geometry
publication date: 1999-11-23T00:00:00Z
review text: The Nieto quintic \(N\) is the subvariety of \(\mathbb{P}^5\) of equations \(\sum^5_{i=0}x_i= \sum^5_{i=0} x_0\dots \widehat x_i\dots x_5=0\). In this paper the author studies a birational model \(\overline N\) of \(N\) (obtained by blowing up some singular points and blowing down some lines) and he proves that \(\overline N\) is the Satake compactification of a ball quotient. On the other hand it follows from results of Barth and Nieto that \(\overline N\) is also a smooth compactification of a quotient of the Siegel space, so \(N\) is Janus-like. The proof is based on the construction of a suitable branched cover of \(\overline N\) and on results of \textit{B. Hunt}: ``The geometry of some special quotients'', Lect. Notes Math. 1637 (1996; Zbl 0904.14025).
Mathematics Subject Classification ID: 14J35
Mathematics Subject Classification ID: 14M17
Mathematics Subject Classification ID: 14J10
Mathematics Subject Classification ID: 32J05
zbMATH DE Number: 1368010
zbMATH Keywords: Nieto quintic
reviewed by: Luciana Picco Botta
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.4310/jdg/1214424969
OpenAlex ID: W1557551816
Wikidata QID: Q115194362
DOI: 10.4310/JDG/1214424969
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description: scientific article; zbMATH DE number 1368010