Higher direct images of dualizing sheaves III
Algebraic Geometry
2025-09-03 v2
Abstract
We show that for flat morphisms between varieties with rational singularities, the higher direct images of the structure sheaf are locally free. As a consequence, the identity component of the relative Picard scheme is a smooth algebraic group scheme. v.2. Bhatt pointed out that Lemma 9 was incorrect; it is now replaced. The main theorem is unchanged.
Keywords
Cite
@article{arxiv.2508.16507,
title = {Higher direct images of dualizing sheaves III},
author = {János Kollár and Sándor J. Kovács},
journal= {arXiv preprint arXiv:2508.16507},
year = {2025}
}