A threefold of general type with \(q_1 = q_2 = p_g = P_2 = 0\)
type: Item
instance of: scholarly article
title: A threefold of general type with \(q_1 = q_2 = p_g = P_2 = 0\)
zbMATH Open document ID: 1051.14047
DOI: 10.1023/A:1022336011727
author: M. Cristina Ronconi
published in: Acta Applicandae Mathematicae
publication date: 2003-04-27T00:00:00Z
review text: The author contructs a smooth projective complex threefold of general type \(X\) such that \(h^i({\mathcal O}_X)=0\) for \(i>0\) and \(h^0(K_X)=h^0(2K_X)=0\). This is in contrast with the case of surfaces, since for a surface of general type \(S\) one always has \(h^0(2K_S)>0\). In the paper it is also shown that the \(m\)-canonical map of the example constructed is birational if and only if \(m\geq 14\). The example arises as a desingularization of a hypersurface of degree 10 in \(4\)-dimensional projective space.
reviewed by: Rita Pardini
Mathematics Subject Classification ID: 14J30
Mathematics Subject Classification ID: 14E05
Mathematics Subject Classification ID: 14J70
zbMATH DE Number: 1901296
zbMATH Keywords: threefold of general type
zbMATH Keywords: plurigenera
zbMATH Keywords: pluricanonical maps
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1901296