The moduli of curves is stably rational for g\(\leq 6\)
type: Item
instance of: scholarly article
title: The moduli of curves is stably rational for g\(\leq 6\)
zbMATH Open document ID: 0576.14027
DOI: 10.1215/S0012-7094-84-05113-5
published in: Duke Mathematical Journal
publication date: 1984-01-01T00:00:00Z
review text: We assume that everything is defined over an algebraically closed field F. An algebraic variety X is called ''stably rational'' over F if \(X\times {\mathbb{P}}^ k\) is birational to \({\mathbb{P}}^ n\) for some k and n. Now, let \({\mathcal M}_ g(F)\) be the moduli space of curves of genus g over F. It is known that \({\mathcal M}_ g(F)\) is rational for \(g=1,2\), and that it is unirational for \(g\leq 10\). In this paper it is proved that \({\mathcal M}_ g(F)\) is stably rational over F for \(g\leq 6\).
Mathematics Subject Classification ID: 14H10
Mathematics Subject Classification ID: 14M20
zbMATH DE Number: 3920654
zbMATH Keywords: stable rationality
zbMATH Keywords: moduli space of curves
zbMATH Keywords: genus
author: János Kollár
author: Frank-Olaf Schreyer
reviewed by: Shoji Koizumi
MaRDI profile type: Publication
cites work: Q3957067
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full work available at URL: s0012-7094-84-05113-5
OpenAlex ID: W1980270816
description: scientific article; zbMATH DE number 3920654