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arXiv · 1103.1704

Inequalities for the Hodge numbers of irregular compact Kaehler manifolds

Luigi Lombardi
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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.

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Luigi Lombardi. 2011-03-09. Inequalities for the Hodge numbers of irregular compact Kaehler manifolds. https://doi.org/10.1093/imrn%2Frnr247

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