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Sia $X$ una varietà abeliana e $L$ un fibrato in rette ampio di tipo $(2, 2 d_{2}, \dots, 2 d_{g})$ su $X$ ; sia $φ_{L}$ l'applicazione associata a $L$ . In questo lavoro si dimostra il seguente fatto: se $d_{i} \leq 2$ per qualsiasi $i$ , $L$ non è mai normalmente generato (quindi, se $φ_{L}$ è un embedding, $φ_{L} (X)$ non è proiettivamente normale); negli altri casi invece $L$ è normalmente generato per $(X, c_{1} (L))$ generico nello spazio dei moduli delle varietà abeliane polarizzate di tipo $(2, 2 d_{2}, \dots, 2 d_{g})$ .

Propriétés et applications de certaines fonctions analogues à la fonction $Θ$ , seconde partie

Elliot (1882)

Annales scientifiques de l'École Normale Supérieure

Propriétés et applications de certaines fonctions analogues à la fonction $Θ$

Elliot (1882)

Annales scientifiques de l'École Normale Supérieure

Prym Subvarieties $P_{λ}$ of Jacobians via Schur correspondences between curves

Yashonidhi Pandey (2010)

Annales de la faculté des sciences de Toulouse Mathématiques

Let $π : Z \to X$ denote a Galois cover of smooth projective curves with Galois group $W$ a Weyl group of a simple Lie group $G$ . For a dominant weight $λ$ , we consider the intermediate curve $Y_{λ} = Z / Stab (λ)$ . One defines a Prym variety $P_{λ} \subset Jac (Y_{λ})$ and we denote by $ϕ_{λ}$ the restriction of the principal polarization of $Jac (Y_{λ})$ upon $P_{λ}$ . For two dominant weights $λ$ and $μ$ , we construct a correspondence $S_{λ μ}$ on $Y_{λ} \times Y_{μ}$ and calculate the pull-back of $ϕ_{μ}$ by $S_{λ μ}$ in terms of $ϕ_{λ}$ .

Prym varietes of bi-elliptic curves.

Juan-Carlos Naranjo (1992)

Journal für die reine und angewandte Mathematik

Prym Varieties and the Geodesic Flow on SO(n).

Stefanos Pantazis (1985/1986)

Mathematische Annalen

Prym Varieties and the Schottky Problem.

Arnaud Beauville (1977)

Inventiones mathematicae

Prym varieties of pairs of coverings.

Lange, Herbert, Recillas, Sevin (2004)

Advances in Geometry

Prym Varieties of Triple Cyclic Covers.

Carel Faber (1988)

Mathematische Zeitschrift

Prym-Tjurin varieties and the Hitchin map.

Renata Scognamillo (1995)

Mathematische Annalen

Pryum varieties and the Verlinde formula.

Bert van Geemen, Emma Previato (1992)

Mathematische Annalen

Pseudo-abelian varieties

Burt Totaro (2013)

Annales scientifiques de l'École Normale Supérieure

Chevalley’s theorem states that every smooth connected algebraic group over a perfect field is an extension of an abelian variety by a smooth connected affine group. That fails when the base field is not perfect. We define a pseudo-abelian variety over an arbitrary field $k$ to be a smooth connected $k$ -group in which every smooth connected affine normal $k$ -subgroup is trivial. This gives a new point of view on the classification of algebraic groups: every smooth connected group over a field is an extension...

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