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Extendability of normal functions associated to algebraic cycles. (English) Zbl 0545.14017
Topics in transcendental algebraic geometry, Ann. Math. Stud. 106, 269-288 (1984).
[For the entire collection see Zbl 0528.00004.]
The article gives the construction of Deligne’s groups, for a smooth proper variety, as extensions of Hodge cycles and intermediate Jacobians; the groups have a cup-product and a cycle class. - For a family f:\(X\to D\) over a disc in \({\mathbb{C}}\), smooth and proper over \(D^*=D-\{0\}\), a logarithmic relative version of Deligne’s groups is used to obtain, for a cycle cohomologous to zero on \(X^*=f^{-1}(D^*)\), a class in the generalized intermediate Jacobian.

MSC:
14Pxx Real algebraic and real-analytic geometry
32J25 Transcendental methods of algebraic geometry (complex-analytic aspects)
14C99 Cycles and subschemes
14D99 Families, fibrations in algebraic geometry
14K30 Picard schemes, higher Jacobians