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Hypergeometric Abelian Varieties

Canadian Journal of Mathematics, 2003
AbstractIn this paper, we construct abelian varieties associated to Gauss’ and Appell–Lauricella hypergeometric series. Abelian varieties of this kind and the algebraic curves we define to construct them were considered by several authors in settings ranging from monodromy groups (Deligne, Mostow), exceptional sets (Cohen, Wolfart, Wüstholz), modular ...
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Moduli of Abelian Varieties

The Annals of Mathematics, 1980
On extra components in the functorial compactification of Ag.- On Mumford's uniformization and Neron models of Jacobians of semistable curves over complete rings.- Torelli theorem via Fourier-Mukai transform.- On the Andre-Oort conjecture for Hilbert modular surfaces.- Toroidal resolutions for some matrix singularities.- Formal Brauer groups and moduli
Norman, P, OORT, F
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Abelian Varieties

2006
AbstractHistorically, Mukai's equivalence with the Poincare bundle on the product of an abelian variety and its dual as kernel was the fist Fourier-Mukai transform. The first section in this chapter functions as a reminder of the basic facts from the rich theory of abelian varieties, and the case of principally polarized abelian varieties is studied. A
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Multiplication Over Abelian Varieties

American Journal of Mathematics, 1988
Sei X eine Abelsche Varietät über einem algebraisch abgeschlossenen Körper. Für Linienbündel L und M auf X betrachtet man die globalen Schnitte \(\Gamma\) (X,L), \(\Gamma\) (X,M) und \(\Gamma\) (X,L\(\otimes M)\). Der Autor untersucht die Surjektivität der Multiplikationsabbildung \(\Gamma\) (X,L)\(\otimes \Gamma (X,M)\to \Gamma (X,L\otimes M)\) für ...
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Abelian Varieties

1995
The series is aimed specifically at publishing peer reviewed reviews and contributions presented at workshops and conferences. Each volume is associated with a particular conference, symposium or workshop. These events cover various topics within pure and applied mathematics and provide up-to-date coverage of new developments, methods and applications.
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Semi-abelian Varieties

2014
In the forthcoming two chapters semi-abelian varieties play an important role. For that purpose we here give a notion of semi-abelian varieties from the viewpoint of complex geometry.
Junjiro Noguchi, Jörg Winkelmann
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Pseudo-Abelian varieties

Mathematical Proceedings of the Cambridge Philosophical Society, 1954
It is a familiar fact that the Picard surface (or hyperelliptic surface of rank 1) admits a completely transitive permutable continuous group of ∞2 automorphisms. There are, however, other non-scrollar surfaces which possess continuous groups of automorphisms, namely, the elhptic surfaces.
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Abelian Varieties.

The American Mathematical Monthly, 1960
Edward H. Batho, Serge Lang
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Polylogarithmic Currents on Abelian Varieties

2000
We construct a certain collection of currents on a universal family of abelian varieties. The cohomology classes of these currents are rational; so our currents are a natural generalization of the Eisenstein series on the modular curve.
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