An effective version of Nori's theorem
type: Item
instance of: scholarly article
title: An effective version of Nori's theorem
zbMATH Open document ID: 0790.14005
DOI: 10.1007/BF02572387
author: M. S. Ravi
published in: Mathematische Zeitschrift
publication date: 1994-06-20T00:00:00Z
full work available at URL: https://eudml.org/doc/174551
review text: Recently, \textit{M. V. Nori} [Invent. Math. 111, No. 2, 349-373 (1993)] has shown that a homologically non-trivial cycle on a projective variety \(X\) is algebraically nontrivial on \(Y=X \cap D_ 1\cap \cdots \cap D_ h\), where the \(D_ i\) are divisors on \(X\) of large enough degree. We give a sufficient condition on the positivity of the divisors \(D_ i\), for Nori's theorem to be applicable. - The main ingredient is an effective vanishing theorem for some Koszul type cohomology groups. We also prove an extension of our vanishing theorem which addresses a conjecture of Nori.
Mathematics Subject Classification ID: 14C25
Mathematics Subject Classification ID: 14F17
Mathematics Subject Classification ID: 14C20
zbMATH DE Number: 561282
zbMATH Keywords: Koszul cohomology groups
zbMATH Keywords: non-trivial cycle
zbMATH Keywords: positivity of divisors
zbMATH Keywords: effective vanishing theorem
MaRDI profile type: Publication
cites work: Syzygies and Koszul cohomology of smooth projective varieties of arbitrary dimension
cites work: Q4285478
cites work: Algebraic cycles and Hodge theoretic connectivity
cites work: Vanishing theorems on complex manifolds
description: scientific article; zbMATH DE number 561282