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Elliptic sufaces with a nef line bundle of genus two.

Antonio Lanteri, Cristina Turrini (1998)

Collectanea Mathematica

Complex projective elliptic surfaces endowed with a numerically effective line bundle of arithmetic genus two are studied and partially classified. A key role is played by elliptic quasi-bundles, where some ideas developed by Serrano in order to study ample line bundles apply to this more general situation.

Equivalence of families of singular schemes on threefolds and on ruled fourfolds.

Flaminio Flamini (2004)

Collectanea Mathematica

The main purpose of this paper is twofold. We first analyze in detail the meaningful geometric aspect of the method introduced in [12], concerning families of irreducible, nodal curves on a smooth, projective threefold X. This analysis gives some geometric interpretations not investigated in [12] and highlights several interesting connections with families of other singular geometric objects related to X and to other varieties. Then we use this method to study analogous problems for families of...

Fonction de Seshadri arithmétique en géométrie d’Arakelov

Huayi Chen (2014)

Annales de la faculté des sciences de Toulouse Mathématiques

To any adelic invertible sheaf on a projective arithmetic variety and any regular algebraic point of the arithmetic variety, we associate a function defined on which measures the separation of jets on this algebraic point by the “small” sections of the adelic invertible sheaf. This function will be used to study the arithmetic local positivity.

Formules de Jacobi et méthodes analytiques

Hai Zhang (2005)

Colloquium Mathematicae

On se propose de retrouver, via des méthodes d'inspiration analytiques basées sur l'utilisation de formules de représentation intégrale attachées à des applications holomorphes propres d'un ouvert de ℂⁿ dans ℂⁿ, les formules de Jacobi généralisées obtenues par C. A. Berenstein, A. Vidras et A. Yger; le fait de disposer de telles preuves (basées sur un raisonnement limité au cadre strictement affine et ne nécessitant pas le recours à une compactification) autorise l'extension de ces résultats au...

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