Displaying similar documents to “Obstructions to deforming curves on a 3 -fold, II: Deformations of degenerate curves on a del Pezzo 3 -fold”

Computing limit linear series with infinitesimal methods

Laurent Evain (2007)

Annales de l’institut Fourier

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Alexander and Hirschowitz determined the Hilbert function of a generic union of fat points in a projective space when the number of fat points is much bigger than the greatest multiplicity of the fat points. Their method is based on a lemma which determines the limit of a linear system depending on fat points approaching a divisor. Other Hilbert functions were computed previously by Nagata. In connection with his counter-example to Hilbert’s fourteenth problem, Nagata determined...

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....

Adjoint representation of E 8 and del Pezzo surfaces of degree 1

Vera V. Serganova, Alexei N. Skorobogatov (2011)

Annales de l’institut Fourier

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Let X be a del Pezzo surface of degree 1 , and let G be the simple Lie group of type E 8 . We construct a locally closed embedding of a universal torsor over X into the G -orbit of the highest weight vector of the adjoint representation. This embedding is equivariant with respect to the action of the Néron-Severi torus T of X identified with a maximal torus of G extended by the group of scalars. Moreover, the T -invariant hyperplane sections of the torsor defined by the roots of G are the...

Exceptional singular ℚ -homology planes

Karol Palka (2011)

Annales de l’institut Fourier

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We consider singular ℚ -acyclic surfaces with smooth locus of non-general type. We prove that if the singularities are topologically rational then the smooth locus is ℂ 1 - or ℂ * -ruled or the surface is up to isomorphism one of two exceptional surfaces of Kodaira dimension zero. For both exceptional surfaces the Kodaira dimension of the smooth locus is zero and the singular locus consists of a unique point of type A 1 and A 2 respectively.

On Halphen’s Theorem and some generalizations

Alcides Lins Neto (2006)

Annales de l’institut Fourier

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Let M n be a germ at 0 ∈ ℂ m of an irreducible analytic set of dimension n , where n ≥ 2 and 0 is a singular point of M . We study the question: when does there exist a germ of holomorphic map φ : ( ℂ n , 0 ) → ( M , 0 ) such that φ - 1 ( 0 ) = { 0 } ? We prove essentialy three results. In Theorem 1 we consider the case where M is a quasi-homogeneous complete intersection of k polynomials F = ( F 1 , ... , F k ) , that is there exists a linear holomorphic vector field X on ℂ m , with eigenvalues λ 1 , ... , λ m ∈ ℚ + such that X ( F T ) = U · F T , where U is a k × k matrix with entries in 𝒪 m . We prove that if...