On polarized manifolds of \(\Delta\) -genus two. I
type: Item
instance of: scholarly article
title: On polarized manifolds of \(\Delta\) -genus two. I
zbMATH Open document ID: 0549.14003
author: Takao Fujita
published in: Journal of the Mathematical Society of Japan
publication date: 1984-01-01T00:00:00Z
review text: Given an ample line bundle L on a projective manifold M, the \(\Delta\) - genus of the polarized manifold (M,L) is defined by \(\Delta (M,L)=n+L^ n-h^ 0(M,L),\) where \(n=\dim M\). Polarized manifolds with \(\Delta\leq 1\) were classified by the author. This article is devoted to the case \(\Delta =2\). In {\S} 0 the classification is briefly outlined. The subsequent sections are devoted to the case in which \(\dim Bs| L| >0\) and \(L^ n>1\). It is first shown that \(| L|\) yields a certain fibration of M with fiber being curves. Thereafter the case of hyperelliptic fibration is precisely described and completely classified. Finally deformations of them are studied.
Mathematics Subject Classification ID: 14C20
Mathematics Subject Classification ID: 14J10
Mathematics Subject Classification ID: 14D99
zbMATH DE Number: 3875434
zbMATH Keywords: \(\Delta\) -genus
zbMATH Keywords: polarized manifold
zbMATH Keywords: hyperelliptic fibration
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2969/jmsj/03640709
OpenAlex ID: W1970298320
DOI: 10.2969/JMSJ/03640709
description: scientific article; zbMATH DE number 3875434