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A higher Albanese map for complex threefolds based on a construction by M. Green

Lorenz Schneider (2005)

Fundamenta Mathematicae

We construct a higher Abel-Jacobi map for 0-cycles on complex threefolds and prove that it can be used to describe Mumford's pull-back of a differential form, and that its image is infinite-dimensional in many cases. However, making a certain assumption, we show that it is not always injective.

Algebraic cycles on abelian varieties and their decomposition

Giambattista Marini (2004)

Bollettino dell'Unione Matematica Italiana

For an Abelian Variety X , the Künneth decomposition of the rational equivalence class of the diagonal Δ X × X gives rise to explicit formulas for the projectors associated to Beauville's decomposition (1) of the Chow ring C H X , in terms of push-forward and pull-back of m -multiplication. We obtain a few simplifications of such formulas, see theorem (4) below, and some related results, see proposition (9) below.

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