Geodesic
Corestriction of central simple algebras and families of Mumford-type
Atti della Accademia nazionale dei Lincei. Rendiconti Lincei. Matematica e applicazioni, Série 9, Tome 10 (1999) no. 3, pp. 191-211

Voir la notice de l'article provenant de la source Biblioteca Digitale Italiana di Matematica

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 \( CM \)-fibers and we give a method to construct a family of Mumford-type starting from such a fiber. 
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     author = {Galluzzi, Federica},
     title = {Corestriction of central simple algebras and families of {Mumford-type}},
     journal = {Atti della Accademia nazionale dei Lincei. Rendiconti Lincei. Matematica e applicazioni},
     pages = {191--211},
     publisher = {mathdoc},
     volume = {Ser. 9, 10},
     number = {3},
     year = {1999},
     zbl = {1023.14021},
     mrnumber = {MR1769159},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/RLIN_1999_9_10_3_a3/}
}
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Galluzzi, Federica. Corestriction of central simple algebras and families of Mumford-type. Atti della Accademia nazionale dei Lincei. Rendiconti Lincei. Matematica e applicazioni, Série 9, Tome 10 (1999) no. 3, pp. 191-211. http://geodesic.mathdoc.fr/item/RLIN_1999_9_10_3_a3/