Pluricanonical systems on irregular 3-folds of general type
type: Item
instance of: scholarly article
title: Pluricanonical systems on irregular 3-folds of general type
zbMATH Open document ID: 1195.14018
published in: Mathematische Zeitschrift
publication date: 2010-05-10T00:00:00Z
review text: Let \(X\) be a smooth projective variety of dimension \(n\) of general type defined over the field of complex numbers. Then for all sufficiently large \(m\), the pluricanonical system \(|mK_{X}|\) defines a birational map \(\varphi_{m}:X\to \mathbb{P}^{N}\) to a projective space \(\mathbb{P}^{N}\). Then it is natural to find an effective bound for such integers \(m\). When \(X\) is a curve, \(\varphi_{m}\) is an embedding for any \(m\geq 3\). For the case of \(\dim X=2\), the map \(\varphi_{m}\) is birational for any \(m\geq 5\). In this paper, the authors studied the case of irregular \(3\)-folds and they obtained the following result. Let \(X\) be an irregular smooth projective variety of general type with \(\dim X=3\) and \(\chi(\omega_{X})>0\). Then the rational map defined by \(|mK_{X}+P|\) is birational for any \(m\geq 5\) and any \(P\in \text{Pic}^{0}(X)\).
reviewed by: Yoshiaki Fukuma
Mathematics Subject Classification ID: 14E05
Mathematics Subject Classification ID: 14C20
Mathematics Subject Classification ID: 14J30
zbMATH DE Number: 5706069
zbMATH Keywords: irregular varieties
zbMATH Keywords: general type
zbMATH Keywords: pluricanonical systems
author: Jungkai A. Chen
author: Christopher Hacon
MaRDI profile type: Publication
full work available at URL: s00209-006-0028-9
OpenAlex ID: W2090546864
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DOI: 10.1007/S00209-006-0028-9
description: scientific article; zbMATH DE number 5706069