Displaying similar documents to “Degeneracy of entire curves in log surfaces with q ¯ = 2 ”

Logarithmic Surfaces and Hyperbolicity

Gerd Dethloff, Steven S.-Y. Lu (2007)

Annales de l’institut Fourier

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In 1981 J. Noguchi proved that in a logarithmic algebraic manifold, having logarithmic irregularity strictly bigger than its dimension, any entire curve is algebraically degenerate. In the present paper we are interested in the case of manifolds having logarithmic irregularity equal to its dimension. We restrict our attention to Brody curves, for which we resolve the problem completely in dimension 2: in a logarithmic surface with logarithmic irregularity...

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...

Finiteness results for Teichmüller curves

Martin Möller (2008)

Annales de l’institut Fourier

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We show that for each genus there are only finitely many algebraically primitive Teichmüller curves C , such that (i) C lies in the hyperelliptic locus and (ii) C is generated by an abelian differential with two zeros of order g - 1 . We prove moreover that for these Teichmüller curves the trace field of the affine group is not only totally real but cyclotomic.

Torsion and Tamagawa numbers

Dino Lorenzini (2011)

Annales de l’institut Fourier

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Let K be a number field, and let A / K be an abelian variety. Let c denote the product of the Tamagawa numbers of A / K , and let A ( K ) tors denote the finite torsion subgroup of A ( K ) . The quotient c / | A ( K ) tors | is a factor appearing in the leading term of the L -function of A / K in the conjecture of Birch and Swinnerton-Dyer. We investigate in this article possible cancellations in this ratio. Precise results are obtained for elliptic curves over ℚ or quadratic extensions K / ℚ , and for abelian surfaces A / ℚ . The smallest possible...

The Frobenius action on rank 2 vector bundles over curves in small genus and small characteristic

Laurent Ducrohet (2009)

Annales de l’institut Fourier

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Let X be a general proper and smooth curve of genus 2 (resp. of genus 3 ) defined over an algebraically closed field of characteristic p . When 3 ≤ p ≤ 7 , the action of Frobenius on rank 2 semi-stable vector bundles with trivial determinant is completely determined by its restrictions to the 30 lines (resp. the 126 Kummer surfaces) that are invariant under the action of some order 2 line bundle over X . Those lines (resp. those Kummer surfaces) are closely related to the elliptic curves (resp....