Hodge sheaves underlying flat projective families
Abstract
We show that, for any fixed weight, there is a natural system of Hodge sheaves, whose Higgs field has no poles, arising from a flat projective family of varieties parametrized by a regular complex base scheme, extending the analogous classical result for smooth projective families due to Griffiths. As an application, based on positivity of direct image sheaves, we establish a criterion for base spaces of rational Gorenstein families to be of general type. A key component of our arguments is centered around the construction of derived categorical objects generalizing relative logarithmic forms for smooth maps and their functorial properties.
Cite
@article{arxiv.2103.03515,
title = {Hodge sheaves underlying flat projective families},
author = {Sándor J. Kovács and Behrouz Taji},
journal= {arXiv preprint arXiv:2103.03515},
year = {2023}
}
Comments
More streamlined exposition following referee's suggestions. Corrected some minor errors in Sections 4 and 5. Main results and statements unchanged