On the class of some projective varieties
type: Item
instance of: scholarly article
title: On the class of some projective varieties
zbMATH Open document ID: 0892.14023
author: E. Ballico
author: Marina Bertolini
author: Cristina Turrini
published in: Collectanea Mathematica
publication date: 1996-11-21T00:00:00Z
full work available at URL: https://eudml.org/doc/40573
review text: Recall that the class of an integral variety \(Y\subset \mathbb{P}^N\) is the degree of the dual variety \(Y^* \subset \mathbb{P}^{N^*}\) if \(Y^*\) is a hypersurface, 0 otherwise. Here we prove some inequalities between the class and the degree of a smooth complex projective manifold and apply them to particular classes of varieties (e.g. scrolls and varieties with low sectional genus). For instance we prove that for a smooth linearly normal complex variety \(X \subset \mathbb{P}^N\) with degree \(d\), class \(\mu\) and dimension \(r\) (hence codimension \(c:= N-r)\) we have \(\mu\leq d(2d+ c-2 )^{2r}/ (4cd)^r \).
Mathematics Subject Classification ID: 14N05
Mathematics Subject Classification ID: 14M07
zbMATH DE Number: 937446
zbMATH Keywords: very ample line bundle
zbMATH Keywords: jet bundle
zbMATH Keywords: class of integral variety
zbMATH Keywords: dual variety
zbMATH Keywords: degree
zbMATH Keywords: scrolls
zbMATH Keywords: varieties with low sectional genus
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 937446