Inequalities for the Hodge numbers of irregular compact Kaehler manifolds

Abstract

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.

15 pages

References in corpus (2)

• Derivative complex, BGG correspondence, and numerical inequalities for compact Kähler manifolds
• On the bicanonical map of irregular varieties

Cited by in corpus (2)

• Grassmannian BGG Complexes and Hodge numbers of irregular varieties
• Complements and higher resonance varieties of hyperplane arrangements