Rational Integrals of the second kind on a complex projective manifold and its primitive cohomology

Details Rational Integrals of the second kind on a complex projective manifold and its primitive cohomology Rational Integrals of the second kind on a complex projective manifold and its primitive cohomology

2007-11-08

arxiv.org/abs/0711.1205v1

Mathematics

Algebraic Geometry

42 pages

Scientific paper

Let X be a complex algebraic manifold of dimension n+1 embedded in a sufficiently higher dimensional complex projective space, and Y a generic hyperplane section of X. We describe the mixed Hodge structure on H^p(X-Y,C) and the Hodge filtration of the middle primitive cohomology group H^n(Y,C)_0 of Y in terms of rational integrals on X. (Key words: Primitive cohomology, Rational integral of the 2nd kind, Generalized Poincare residue map, Hodge filtration, Mixed Hodge structure)

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