\#-minimal models of uniruled 3-folds
type: Item
instance of: scholarly article
title: \#-minimal models of uniruled 3-folds
zbMATH Open document ID: 1054.14053
author: Massimiliano Mella
published in: Mathematische Zeitschrift
publication date: 2004-06-17T00:00:00Z
review text: Let \(T\) be a terminal \(\mathbb{Q}\)-factorial uniruled 3-fold and let \(\mathbf H\) be a nef movable linear system on \(T\). According to \textit{M. Reid} [Math. Ann. 275, 71--80 (1986; Zbl 0579.14017)], a \(\#\)-minimal model of the pair \((T, {\mathbf H})\) is a suitable pair \((T^{\#}, {\mathbf H}^{\#})\) such that there is a birational map \(\phi: T\to T^{\#}\) with \(\phi_*{\mathbf H}= {\mathbf H}^{\#}\). In this paper, the author proves the existence of \(\#\)-minimal models and he classifies them when \(\mathbf H\) is nef and big and the generic \(H\in{\mathbf H}\) is a smooth surface of negative Kodaira dimension. Moreover, he lists all possible \(\#\)-minimal models of small degree 3-folds embedded in projective spaces.
reviewed by: Luciana Picco Botta
Mathematics Subject Classification ID: 14J30
Mathematics Subject Classification ID: 14N05
Mathematics Subject Classification ID: 14E30
zbMATH DE Number: 2075749
MaRDI profile type: Publication
full work available at URL: s002090100374
OpenAlex ID: W1982786673
DOI: 10.1007/S002090100374
description: scientific article; zbMATH DE number 2075749