Birational geometry of quartic 3-folds. II: The importance of being \(\mathbb{Q}\)-factorial
type: Item
instance of: scholarly article
title: Birational geometry of quartic 3-folds. II: The importance of being \(\mathbb{Q}\)-factorial
zbMATH Open document ID: 1058.14022
author: Massimiliano Mella
published in: Mathematische Annalen
publication date: 2004-10-01T00:00:00Z
review text: The author studies the birational geometry of a \(\mathbb Q\)-factorial quartic 3-fold \(X\subset \mathbb P^4_k\) with only ordinary double points as singularities, where \(k\) is either \(\mathbb C\) or a (not necessarily algebraically closed) field of characteristic 0. He proves that such a 3-fold is birationally rigid, i.e., any birational map \(X\to V\) to a Mori fibre space is a self map. The main tools used in the proof are: 1) the maximal singularities with center of positive dimension: in this case the centers are shown to be lines through some singular point: 2) the Sarkisov links, which give the required self maps \(X\to V\) to a Mori fibre space.
Mathematics Subject Classification ID: 14E07
Mathematics Subject Classification ID: 14J30
Mathematics Subject Classification ID: 14E30
zbMATH DE Number: 2104999
zbMATH Keywords: birationally rigid
zbMATH Keywords: Mori fibre space
zbMATH Keywords: Sarkisov links
reviewed by: Luciana Picco Botta
MaRDI profile type: Publication
full work available at URL: s00208-004-0542-1
OpenAlex ID: W2083825449
DOI: 10.1007/S00208-004-0542-1
description: scientific article; zbMATH DE number 2104999