Displaying similar documents to “A geometric description of Hazama's exceptional classes”

Hodge Classes and Abelian Varieties of Quaternionic Type

Giuseppe Lombardo (2006)

Bollettino dell'Unione Matematica Italiana

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We obtain coniugacy classes (with respect to a 𝔰 ⁢ l 2 action) in the space of Hodge cycles in the middle cohomology of an Abelian variety of quaternionic type. The existence of such a class simplifies the study of the Hodge conjecture.

Corestriction of central simple algebras and families of Mumford-type

Federica Galluzzi (1999)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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Let M be a family of Mumford-type, that is, a family of polarized complex abelian fourfolds as introduced by Mumford in [9]. This family is defined starting from a quaternion algebra A over a real cubic number field and imposing a condition to the corestriction of such A . In this paper, under some extra conditions on the algebra A , we make this condition explicit and in this way we are able to describe the polarization and the complex structures of the fibers. Then, we look at the non...

Algebraic cycles on abelian varieties and their decomposition

Giambattista Marini (2004)

Bollettino dell'Unione Matematica Italiana

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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.