On a question of Miles Reid
type: Item
instance of: scholarly article
title: On a question of Miles Reid
zbMATH Open document ID: 0961.14021
author: Kazuhiro Konno
author: Margarida Mendes Lopes
published in: Manuscripta Mathematica
publication date: 2001-06-05T00:00:00Z
review text: Let \(f:S\to B\) be a relatively minimal fibration, where \(S\) (respectively \(B)\) is a non-singular projective surface (respectively curve) and suppose that the general fibre of \(f\) is a smooth, irreducible curve of genus \(g\geq 2\). Let \({\mathcal R}(f)= \bigoplus_{n\geq 0} f_*(K^{\otimes n}_{S |B})\) the relative canonical algebra. Some years ago \textit{M. Reid} [``Problems on pencils of small genus'' (Preprint 1990)] asked whether \({\mathcal R}(f)\) is always generated in degree 1, 2 and 3. In this paper the authors present explicit counter-examples (of hyperelliptic and non-hyperelliptic fibrations of unbounded genus) to the above conjecture.
Mathematics Subject Classification ID: 14J10
Mathematics Subject Classification ID: 14D06
Mathematics Subject Classification ID: 14J29
Mathematics Subject Classification ID: 14H10
zbMATH DE Number: 1355507
zbMATH Keywords: minimal fibration
reviewed by: A. Del Centina
MaRDI profile type: Publication
full work available at URL: s002290050196
OpenAlex ID: W2023022616
DOI: 10.1007/S002290050196
description: scientific article; zbMATH DE number 1355507