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complex hypersurfaces — 1 results found.

      
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Lê Cycles and Milnor Classes of Compact Hypersurfaces
C. R. Math. Rep. Acad. Sci. Canada Vol. 34 (2) 2012, pp. 33–38
Roberto Callejas-Bedregal; Michelle F.Z. Morgado; Jose Seade (Received: 2010/11/18, Revised: 2011/02/07)

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We determine the relation amongst the global Lê cycles and the Milnor classes of analytic hypersurfaces defined by a section of a very ample line bundle over a compact complex manifold. The key point is finding appropriate expressions for the global Lê cycles and for the Milnor classes in terms of polar varieties. Our starting points are an interpretation of the Lê cycles given by T. Gaffney and R. Gassler, a formula by A. Parusinski and P. Pragacz for the Milnor classes via McPherson’s functor, and a conjecture of J.-P. Brasselet, that we prove, stating that Milnor classes can be expressed in terms of polar varieties. We then use the work by R. Piegne for Mather classes, by J. Schürmann and M. Tibăr for MacPherson’s classes for constructible functions, and by D. Massey for an extension of the local Lê cycles for constructible sheaves.

Nous déterminons la relation entre les cycles de Lê globaux et les classes de Milnor des hypersurfaces analytiques définies par une section d’un fibré en droites très ample sur des variétés non-singulières complexes compactes. Le point clé consiste à trouver des expressions appropriées des cycles de Lê globaux et des classes de Milnor en termes de variétés polaires. Nos points de départ sont une interprétation des cycles de Lê donnée par T. Gaffney et R. Gassler, une formule de A. Parusinski et P. Pragacz pour les classes de Milnor via le foncteur de McPherson, et une conjecture de J.-P. Brasselet pour les classes de Milnor, que nous démontrons, qui affirme que l’on peut exprimer les classes de Milnor en fonction des classes polaires. Nous utilisons alors des travaux de R. Piene sur les classes de Mather, de J. Schürmann et M. Tibăr sur les classes de MacPherson des fonctions constructibles, et de D. Massey qui généralise les cycles de Lê locaux aux faisceaux constructibles.

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algebraic number theory approximation property automorphisms Bessel functions Boson-fermion correspondence C*-algebra Carmichael number center problem Chebyshev transform classification Classification of simple C*-algebras composition operators continued fractions Cuntz Semigroup elliptic curves fixed point Fourier transform function fields. functoriality general relativity generic property ideals indefinite inner product inductive limits of sub-homogeneous C*- algebras Irrational rotation algebra J-Hermitian matrix K-theory Kahler manifolds L-functions maximal ideal space nonexpansive mapping numerical range orthogonal polynomials Predual space prime number property SP Renormalization rotation algebras Salem number semi-reciprocal polynomials tracially approximate splitting interval algebras unbounded traces uniqueness Weak Markov set Whitney problems

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