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

Inequalities for the Hodge Numbers of Irregular Compact Kähler Manifolds / L. Lombardi. - In: INTERNATIONAL MATHEMATICS RESEARCH NOTICES. - ISSN 1073-7928. - 2013:1(2013), pp. 63-83. [10.1093/imrn/rnr247]

Inequalities for the Hodge Numbers of Irregular Compact Kähler Manifolds

L. Lombardi
2013

Abstract

Based on the work of Lazarsfeld and Popa, we use the derivative complex associated to the bundle of holomorphic p-forms to provide inequalities for all the Hodge numbers of a special class of irregular compact Kahler manifolds. For three-folds and four-folds, we give an asymptotic bound for all the Hodge numbers in terms of the irregularity. As a byproduct, via the Bernstein-Gel'fand-Gel'fand correspondence, we also bound the regularity of the exterior cohomology modules of bundles of holomorphic p-forms.
Hodge numbers, derivative complexes, regularity of cohomology modules
Settore MAT/03 - Geometria
gen-2012
Article (author)
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/2434/638746
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