Rational Integrals of the second kind on a complex projective manifold and its primitive cohomology
Abstract
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(XY,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)
 Publication:

arXiv eprints
 Pub Date:
 November 2007
 arXiv:
 arXiv:0711.1205
 Bibcode:
 2007arXiv0711.1205T
 Keywords:

 Mathematics  Algebraic Geometry;
 Mathematics  Complex Variables;
 14D07;
 32G13
 EPrint:
 42 pages