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A geometric description of Hazama's exceptional classes

Federica Galluzzi — 2000

Bollettino dell'Unione Matematica Italiana

Sia X una varietà abeliana complessa di tipo Mumford. In queste note daremo una descrizione esplicita delle classi eccezionali in B 2 X × X trovate da Hazama in [Ha] e le descriveremo geometricamente usando la grassmaniana delle rette di P 7 .

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

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 simple C M -fibers...

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