On an infinitesimal invariant of normal functions
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.
infinitesimal invariant of normal function
scientific article; zbMATH DE number 4125537
scientific article