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arXiv · 2508.16507

Higher direct images of dualizing sheaves III

János Kollár·Sándor J. Kovács
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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.

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János Kollár, Sándor J. Kovács. 2025-08-22. Higher direct images of dualizing sheaves III. https://arxiv.org/abs/2508.16507

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