Inequalities for the Hodge numbers of irregular compact Kaehler manifolds

Details Inequalities for the Hodge numbers of irregular compact Kaehler manifolds Inequalities for the Hodge numbers of irregular compact Kaehler manifolds

2011-03-09

arxiv.org/abs/1103.1704v1

Int Math Res Notices (2012)

Mathematics

Algebraic Geometry

15 pages

Scientific paper

10.1093/imrn/rnr247

Based on work of R. Lazarsfeld and M. Popa, we use the derivative complex associated to the bundle of the holomorphic p-forms to provide inequalities for all the Hodge numbers of a special class of irregular compact Kaehler manifolds. For 3-folds and 4-folds we give an asymptotic bound for all the Hodge numbers in terms of the irregularity. As a byproduct, via the BGG correspondence, we also bound the regularity of the exterior cohomology modules of bundles of holomorphic p-forms.

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