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Algebraic cobordism of bundles on varieties

Y.-P. Lee, Rahul Pandharipande (2012)

Journal of the European Mathematical Society

The double point relation defines a natural theory of algebraic cobordism for bundles on varieties. We construct a simple basis (over ) of the corresponding cobordism groups over Spec( ) for all dimensions of varieties and ranks of bundles. The basis consists of split bundles over products of projective spaces. Moreover, we prove the full theory for bundles on varieties is an extension of scalars of standard algebraic cobordism.

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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