Displaying similar documents to “Homology classes of real algebraic sets”

Codimension two transcendental submanifolds of projective space

Wojciech Kucharz, Santiago R. Simanca (2010)

Annales de l’institut Fourier

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We provide a simple characterization of codimension two submanifolds of ℙ n ( ℝ ) that are of algebraic type, and use this criterion to provide examples of transcendental submanifolds when n ≥ 6 . If the codimension two submanifold is a nonsingular algebraic subset of ℙ n ( ℝ ) whose Zariski closure in ℙ n ( ℂ ) is a nonsingular complex algebraic set, then it must be an algebraic complete intersection in ℙ n ( ℝ ) .

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...

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...

Whittaker and Bessel functors for G 𝕊 p 4

Sergey Lysenko (2006)

Annales de l’institut Fourier

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The theory of Whittaker functors for G L n is an essential technical tools in Gaitsgory’s proof of the Vanishing Conjecture appearing in the geometric Langlands correspondence. We define Whittaker functors for G 𝕊 p 4 and study their properties. These functors correspond to the maximal parabolic subgroup of G 𝕊 p 4 , whose unipotent radical is not commutative. We also study similar functors corresponding to the Siegel parabolic subgroup of G 𝕊 p 4 , they are related with Bessel models for G 𝕊 p 4 and...