II, Cambridge Studies in Advanced Mathematics, vol. 77, Cambridge University Press, doi: 10.A convex set can have more than one supporting hyperplane at a given point on its boundary. have hyperplanes through a given pint and parallel to a given hyperplane. Voisin, Claire (2003), Hodge theory and complex algebraic geometry. versions of the Hahn-Banach theorem for oriented matrcds of rank three.Sabbah, Claude (2001), Théorie de Hodge et théorème de Lefschetz « difficile » (PDF), archived from the original (PDF) on.51, Princeton University Press, MR 0163331 Milnor, John Willard (1963), Morse theory, Annals of Mathematics Studies, No.sous laction adjointe de G0 dans g0 dapres 11(Theorem 34.4). Émile Borel (in French), Paris: Gauthier-Villars Reprinted in Lefschetz, Solomon (1971), Selected papers, New York: Chelsea Publishing Co., ISBN 978-0-8284-0234-7, MR 0299447 Le fibr T sera dit structure CR de rang maximum sur X si lentier r est. Lefschetz, Solomon (1924), L'Analysis situs et la géométrie algébrique, Collection de Monographies publiée sous la Direction de M.I, Ergebnisse der Mathematik und ihrer Grenzgebiete. Lazarsfeld, Robert (2004), Positivity in algebraic geometry.(1992), "Solomon Lefschetz", in National Academy of Sciences, Office of the Home Secretary (ed.), Biographical Memoirs, vol. 61, The National Academies Press, ISBN 978-6-3 Deligne, Pierre (1980), "La conjecture de Weil.Beauville, Arnaud, The Hodge Conjecture, CiteSeerX 10.1.^ Milnor 1969, p. 39 harvnb error: no target: CITEREFMilnor1969 ( help).4 Ferrand, D.Courbes gauches et fibrs de rang 2. ^ Milnor 1969, Theorem 7.3 and Corollary 7.4 harvnb error: no target: CITEREFMilnor1969 ( help) As an application, we prove the generic vanishing theorem for all normal CohenMacaulay subvarieties.The natural map H k( Y, Z) → H k( X, Z) in singular homology is an isomorphism for k n -adic cohomology of smooth projective varieties over algebraically closed fields of positive characteristic by Pierre Deligne ( 1980).The Lefschetz theorem refers to any of the following statements: Let X be an n-dimensional complex projective algebraic variety in CP N, and let Y be a hyperplane section of X such that U = X ∖ Y is smooth. The Lefschetz hyperplane theorem for complex projective varieties
Similar results have since been found for homotopy groups, in positive characteristic, and in other homology and cohomology theories.Ī far-reaching generalization of the hard Lefschetz theorem is given by the decomposition theorem. A result of this kind was first stated by Solomon Lefschetz for homology groups of complex algebraic varieties. More precisely, the theorem says that for a variety X embedded in projective space and a hyperplane section Y, the homology, cohomology, and homotopy groups of X determine those of Y. In mathematics, specifically in algebraic geometry and algebraic topology, the Lefschetz hyperplane theorem is a precise statement of certain relations between the shape of an algebraic variety and the shape of its subvarieties.
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