Displaying similar documents to “The Frobenius action on rank 2 vector bundles over curves in small genus and small characteristic”

Obstructions to deforming curves on a 3 -fold, II: Deformations of degenerate curves on a del Pezzo 3 -fold

Hirokazu Nasu (2010)

Annales de l’institut Fourier

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We study the Hilbert scheme Hilb s c V of smooth connected curves on a smooth del Pezzo 3 -fold V . We prove that any degenerate curve C , any curve C contained in a smooth hyperplane section S of V , does not deform to a non-degenerate curve if the following two conditions are satisfied: (i) χ ( V , ℐ C ( S ) ) ≥ 1 and (ii) for every line ℓ on S such that ℓ ∩ C = ∅ , the normal bundle N ℓ / V is trivial (  N ℓ / V ≃ 𝒪 ℙ 1 ⊕ 2 ). As a consequence, we prove an analogue (for Hilb s c V ) of a conjecture of J. O. Kleppe, which is concerned with non-reduced components...

Siegel’s theorem and the Shafarevich conjecture

Aaron Levin (2012)

Journal de Théorie des Nombres de Bordeaux

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It is known that in the case of hyperelliptic curves the Shafarevich conjecture can be made effective, i.e., for any number field k and any finite set of places S of k , one can effectively compute the set of isomorphism classes of hyperelliptic curves over k with good reduction outside S . We show here that an extension of this result to an effective Shafarevich conjecture for of hyperelliptic curves of genus g would imply an effective version of Siegel’s theorem for integral points...

Very ampleness of multiples of principal polarization on degenerate Abelian surfaces.

Alessandro Arsie (2005)

Revista Matemática Complutense

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Quite recently, Alexeev and Nakamura proved that if Y is a stable semi-Abelic variety (SSAV) of dimension g equipped with the ample line bundle O(1), which deforms to a principally polarized Abelian variety, then O(n) is very ample as soon as n ≥ 2g + 1, that is n ≥ 5 in the case of surfaces. Here it is proved, via elementary methods of projective geometry, that in the case of surfaces this bound can be improved to n ≥ 3.

A 4₃ configuration of lines and conics in ℙ⁵

Tomasz Szemberg (1994)

Annales Polonici Mathematici

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Studying the connection between the title configuration and Kummer surfaces we write explicit quadratic equations for the latter. The main results are presented in Theorems 8 and 16.

On the extendability of elliptic surfaces of rank two and higher

Angelo Felice Lopez, Roberto Muñoz, José Carlos Sierra (2009)

Annales de l’institut Fourier

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We study threefolds X ⊂ ℙ r having as hyperplane section a smooth surface with an elliptic fibration. We first give a general theorem about the possible embeddings of such surfaces with Picard number two. More precise results are then proved for Weierstrass fibrations, both of rank two and higher. In particular we prove that a Weierstrass fibration of rank two that is not a K3 surface is not hyperplane section of a locally complete intersection threefold and we give some conditions, for many...