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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.

Chern classes of reductive groups and an adjunction formula

Valentina Kiritchenko (2006)

Annales de l’institut Fourier

In this paper, I construct noncompact analogs of the Chern classes for equivariant vector bundles over complex reductive groups. For the tangent bundle, these Chern classes yield an adjunction formula for the (topological) Euler characteristic of complete intersections in reductive groups. In the case where a complete intersection is a curve, this formula gives an explicit answer for the Euler characteristic and the genus of the curve. I also prove that the higher Chern classes vanish. The first...

Direct images in non-archimedean Arakelov theory

Henri Gillet, Christophe Soulé (2000)

Annales de l'institut Fourier

We develop a formalism of direct images for metrized vector bundles in the context of the non-archimedean Arakelov theory introduced in our joint work with S. Bloch. We prove a Riemann-Roch-Grothendieck theorem for this direct image.

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