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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

##### MSC:
 14C99 Cycles and subschemes 14J10 Families, moduli, classification: algebraic theory 14C20 Divisors, linear systems, invertible sheaves
##### Keywords:
algebraic cycle; linear system; normal function