On an infinitesimal invariant of normal functions
type: Item
instance of: scholarly article
title: On an infinitesimal invariant of normal functions
zbMATH Open document ID: 0687.14006
DOI: 10.1007/BF01444525
author: Xian Wu
published in: Mathematische Annalen
publication date: 1990-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/164727
review text: Griffiths' infinitesimal invariant \(\delta\) \(\nu\) associated to a normal function \(\nu\) is one of the latest developments in Hodge theory. The main goal of this paper is to investigate the non-degeneracy of \(\delta\) \(\nu\). More precisely, it proves a theorem which states that \(\delta\) \(\nu\neq 0\) if certain cohomology conditions are satisfied. The theorem is then applied to establish the non-degeneracy of \(\delta\) \(\nu\) in both local and global cases. The results of this paper imply that \(\delta\) \(\nu\) does have geometric significance as expected. The method used in this work also gives a new way to show the non-degeneracy of normal functions and hence may have further applications.
Mathematics Subject Classification ID: 14C30
Mathematics Subject Classification ID: 14C99
Mathematics Subject Classification ID: 14B10
zbMATH DE Number: 4125537
zbMATH Keywords: infinitesimal invariant of normal function
zbMATH Keywords: Hodge theory
MaRDI profile type: Publication
cites work: Q3312351
cites work: Koszul cohomology and the geometry of projective varieties. Appendix: The nonvanishing of certain Koszul cohomology groups (by Mark Green and Robert Lazarsfeld)
cites work: Q3715242
cites work: Griffiths' infinitesimal invariant and the Abel-Jacobi map
cites work: Periods of Integrals on Algebraic Manifolds, I. (Construction and Properties of the Modular Varieties)
cites work: Periods of integrals on algebraic manifolds. III: Some global differential-geometric properties of the period mapping
cites work: A Theorem Concerning the Differential Equations Satisfied by Normal Functions Associated to Algebraic Cycles
cites work: Q3697133
cites work: Q4195061
cites work: Vector bundles on complex projective spaces
cites work: Generalized intermediate Jacobians and the theorem on normal functions
OpenAlex ID: W1969542733
description: scientific article; zbMATH DE number 4125537