Numerical character of the effectivity of adjoint line bundles

Frédéric Campana; Vincent Koziarz; Mihai Păun

Displaying similar documents to “Numerical character of the effectivity of adjoint line bundles”

Pluricanonical maps for threefolds of general type

Gueorgui Tomov Todorov (2007)

Annales de l’institut Fourier

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In this paper we will prove that for a threefold of general type and large volume the second plurigenera is positive and the fifth canonical map is birational.

Orthogonal bundles on curves and theta functions

Arnaud Beauville (2006)

Annales de l’institut Fourier

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Let $ℳ$ be the moduli space of principal ${SO}_{r}$ -bundles on a curve $C$ , and $ℒ$ the determinant bundle on $ℳ$ . We define an isomorphism of $H^{0} (ℳ, ℒ)$ onto the dual of the space of $r$ -th order theta functions on the Jacobian of $C$ . This isomorphism identifies the rational map ${ℳ ⇢ | ℒ |}^{*}$ defined by the linear system $| ℒ |$ with the map $ℳ ⇢ | r Θ |$ which associates to a quadratic bundle $(E, q)$ the theta divisor $Θ_{E}$ . The two components $ℳ^{+}$ and $ℳ^{-}$ of $ℳ$ are mapped into the subspaces of even and odd theta functions respectively. Finally we discuss...

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 $X \subset ℙ^{r}$ 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...

Maximal compatible splitting and diagonals of Kempf varieties

Niels Lauritzen, Jesper Funch Thomsen (2011)

Annales de l’institut Fourier

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Lakshmibai, Mehta and Parameswaran (LMP) introduced the notion of maximal multiplicity vanishing in Frobenius splitting. In this paper we define the algebraic analogue of this concept and construct a Frobenius splitting vanishing with maximal multiplicity on the diagonal of the full flag variety. Our splitting induces a diagonal Frobenius splitting of maximal multiplicity for a special class of smooth Schubert varieties first considered by Kempf. Consequences are Frobenius splitting...

Geometry of the genus 9 Fano 4-folds

Frédéric Han (2010)

Annales de l’institut Fourier

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We study the geometry of a general Fano variety of dimension four, genus nine, and Picard number one. We compute its Chow ring and give an explicit description of its variety of lines. We apply these results to study the geometry of non quadratically normal varieties of dimension three in a five dimensional projective space.