Examples of Mori dream spaces with Picard number two
type: Item
instance of: scholarly article
title: Examples of Mori dream spaces with Picard number two
zbMATH Open document ID: 1304.14020
published in: Manuscripta Mathematica
publication date: 2014-11-13T00:00:00Z
full work available at URL: https://arxiv.org/abs/1304.8005
review text: In the paper under review, the author gives a sufficient condition such that a projective variety with Picard number 2 is a Mori dream space. Using this result, the author shows that intersections of general hyperplanes of low degree in \(\mathbb P ^N\) (or in \(\mathbb P ^1\times \mathbb P ^N\)) are Mori dream spaces. Recall that a Mori dream space is a normal, projective, \(\mathbb Q\)-factorial variety such that \({\text{Pic}}(X)_{\mathbb Q} =N^1(X)_{\mathbb Q}\), \({\text{Nef}}(X)\) is the affine hull of finitely many semiample line bundles and there is a finite collection of small \(\mathbb Q\)-factorial modifications \(f_i:X\dasharrow X_i\) such that \({\text{Mov}}(X)=\bigcup_i f_i^*({\text{Nef}}(X_i))\) where for all \(i\), \({\text{Nef}}(X_i)\) is the affine hull of finitely many semiample line bundles.
Mathematics Subject Classification ID: 14E30
Mathematics Subject Classification ID: 14C20
zbMATH DE Number: 6369208
zbMATH Keywords: Mori dream space
author: Atsushi Ito
reviewed by: Christopher Hacon
MaRDI profile type: Publication
OpenAlex ID: W2120358884
arXiv ID: 1304.8005
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cites work: A Lefschetz hyperplane theorem for Mori dream spaces
cites work: Birational geometry of hypersurfaces in products of projective spaces
cites work: Big rational surfaces
DOI: 10.1007/S00229-014-0673-Y
description: scientific article; zbMATH DE number 6369208