Geometria Complessa e Geometria Differenziale
Geometria Complessa e Geometria Differenziale
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L. Di Cerbo - L. Lombardi

L^2-Betti Numbers and Convergence of Normalized Hodge Numbers via the Weak Generic Nakano Vanishing Theorem

created by daniele on 26 Feb 2020

[BibTeX]

preprint

Inserted: 26 feb 2020
Last Updated: 26 feb 2020

Year: 2019

ArXiv: 1906.06279 PDF

Abstract:

We study the rate of growth of normalized Hodge numbers along a tower of abelian covers of a smooth projective variety with semismall Albanese map. These bounds are in some cases optimal. Moreover, we compute the $L^2$-Betti numbers of irregular varieties that satisfy the weak generic Nakano vanishing theorem e.g., varieties with semismall Albanese map). Finally, we study the convergence of normalized plurigenera along towers of abelian covers of any irregular variety. As an application, we extend a result of Koll\'ar concerning the multiplicativity of higher plurigenera of a smooth projective variety of general type, to a wider class of varieties. In the Appendix, we study irregular varieties for which the first Betti number diverges along a tower of abelian covers induced by the Albanese variety.

Tags: SIR2014-AnHyC

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