Une remarque sur l’invariant infinitésimal des fonctions normales. (A remark on the infinitesimal invariant of normal functions). (French) Zbl 0673.14005

Assume X is a projective variety of dimension 2n, Z is an algebraic cycle on X of dimension n and \(| L|\) is a linear system on X with smooth generic member \(X_ s\) such that Z restricted to \(X_ s\) is homologous to zero. Then one disposes of a “normal function” \(\nu_ Z\) to which one associates the “infinitesimal invariant” \(\delta \nu_ Z\) [cf. P. Griffiths, Compos. Math. 50, 267-324 (1983; Zbl 0576.14009)]. The paper under review provides a simple formula for \(\delta \nu_ Z\). As an application it is shown for instance that if L is “sufficiently ample” and \(H^{n-1}(\Omega_ X^ n)=0\), \(H^ 1({\mathcal O}_ X)=0\) then \(\delta \nu_ Z\) vanishes iff \([Z]\in H^{2n}(X,{\mathbb{Z}})\) is a torsion class.
Reviewer: A.Buium


14C99 Cycles and subschemes
14J10 Families, moduli, classification: algebraic theory
14C20 Divisors, linear systems, invertible sheaves


Zbl 0576.14009