Displaying similar documents to “An interpolation theorem in toric varieties”

On fundamental groups of algebraic varieties and value distribution theory

Katsutoshi Yamanoi (2010)

Annales de l’institut Fourier

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If a smooth projective variety X admits a non-degenerate holomorphic map ℂ → X from the complex plane ℂ , then for any finite dimensional linear representation of the fundamental group of X the image of this representation is almost abelian. This supports a conjecture proposed by F. Campana, published in this journal in 2004.

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...

The membership problem for polynomial ideals in terms of residue currents

Mats Andersson (2006)

Annales de l’institut Fourier

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We find a relation between the vanishing of a globally defined residue current on ℙ n and solution of the membership problem with control of the polynomial degrees. Several classical results appear as special cases, such as Max Nöther’s theorem, for which we also obtain a generalization. Furthermore there are some connections to effective versions of the Nullstellensatz. We also provide explicit integral representations of the solutions.

On the Briançon-Skoda theorem on a singular variety

Mats Andersson, Håkan Samuelsson, Jacob Sznajdman (2010)

Annales de l’institut Fourier

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Let Z be a germ of a reduced analytic space of pure dimension. We provide an analytic proof of the uniform Briançon-Skoda theorem for the local ring 𝒪 Z ; a result which was previously proved by Huneke by algebraic methods. For ideals with few generators we also get much sharper results.

Local characterization of algebraic manifolds and characterization of components of the set S f

Zbigniew Jelonek (2000)

Annales Polonici Mathematici

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We show that every n-dimensional smooth algebraic variety X can be covered by Zariski open subsets U i which are isomorphic to closed smooth hypersurfaces in ℂ n + 1 . As an application we show that forevery (pure) n-1-dimensional ℂ-uniruled variety X ⊂ ℂ m there is a generically-finite (even quasi-finite) polynomial mapping f : ℂ n → ℂ m such that X ⊂ S f . This gives (together with [3]) a full characterization of irreducible components of the set S f for generically-finite polynomial mappings f : ℂ n → ℂ m .