Algebraic Surfaces

Bădescu, Lucian

doi:10.1007/978-1-4757-3512-3

Cited by 162 publications

(244 citation statements)

References 7 publications

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“…(2) X will be a projective algebraic normal surface with at worst canonical singularities (that is, X is smooth or has rational double points; see [Bad01] for details about rational double points), whose canonical divisor K X is ample and base-point-free. (3) We will denote the canonical map of X as ϕ.…”

Section: Preliminaries and Notationmentioning

confidence: 99%

On the bicanonical morphism of quadruple Galois canonical covers

Gallego

Purnaprajna

2011

Trans. Amer. Math. Soc.

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Abstract. In this article we study the bicanonical map ϕ 2 of quadruple Galois canonical covers X of surfaces of minimal degree. We show that ϕ 2 has diverse behavior and exhibits most of the complexities that are possible for a bicanonical map of surfaces of general type, depending on the type of X. There are cases in which ϕ 2 is an embedding, and if it so happens, ϕ 2 embeds X as a projectively normal variety, and there are cases in which ϕ 2 is not an embedding. If the latter, ϕ 2 is finite of degree 1, 2 or 4. We also study the canonical ring of X, proving that it is generated in degree less than or equal to 3 and finding the number of generators in each degree. For generators of degree 2 we find a nice general formula which holds for canonical covers of arbitrary degrees. We show that this formula depends only on the geometric and the arithmetic genus of X.

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Section: Preliminaries and Notationmentioning

confidence: 99%

On the bicanonical morphism of quadruple Galois canonical covers

Gallego

Purnaprajna

2011

Trans. Amer. Math. Soc.

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“…We remark that our work gives also concrete examples of (nef) divisor D with kod(D) = −∞ and ν(D) = 1, for which D · K M > 0 (a class of examples that, as far we know, does not appear in the literature [15], [2]). The examples consist in taking D := K H 5 or D := K H 9 for the modular foliations of Theorem 2 (details are given in Section 3).…”

Section: Birational Characterization Ofmentioning

confidence: 99%

“…Along this section we freely use material from Hirzebruch's paper [9] in order to describe the analytic isomorphism between Y (5, (2)) and the blown up projective plane.…”

Section: Y (5 (2)) As Klein's Icosahedral Surfacementioning

confidence: 99%

Hilbert modular foliations on the projective plane

Mendes¹,

Pereira²

2005

Comment. Math. Helv.

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“…[13], [14]) en les ordonnant selon la classification des surfaces, notamment selon leur dimension de Kodaira notée κ(X ) (cf. [2] et [3]). [12].…”

Section: Exemplesunclassified

Sur le rang des jacobiennes sur un corps de fonctions

Hindry¹

2005

Bul. Soc. Math. France

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Résumé. -Soit f : X → C une surface projective fibrée au-dessus d'une courbe et définie sur un corps de nombres k. Nous donnons une interprétation du rang du groupe de Mordell-Weil sur k(C) de la jacobienne de la fibre générique (modulo la partie constante) en termes de moyenne des traces de Frobenius sur les fibres de f . L'énoncé fournit une réinterprétation de la conjecture de Tate pour la surface X et généralise des résultats de Nagao, Rosen-Silverman et Wazir.Abstract (On the rank of Jacobians on a function field). -Let f : X → C be a projective surface fibered over a curve and defined over a number field k. We give an interpretation of the rank of the Mordell-Weil group over k(C) of the jacobian of the generic fibre (modulo the constant part) in terms of average of the traces of Frobenius on the fibers of f . The results also give a reinterpretation of the Tate conjecture for the surface X and generalizes results of Nagao, Rosen-Silverman and Wazir.Texte reçu le 21 avril

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Algebraic Surfaces

Cited by 162 publications

References 7 publications

On the bicanonical morphism of quadruple Galois canonical covers

On the bicanonical morphism of quadruple Galois canonical covers

Hilbert modular foliations on the projective plane

Sur le rang des jacobiennes sur un corps de fonctions

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