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arXiv · 2509.04382

Differential forms on varieties with pre-$k$-rational singularities

Scott Hiatt
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Abstract

Let $X$ be a complex algebraic variety. With $\mathbb{Q}$-coefficients, the compactly supported cohomology groups $H^{i}_{c}(X, \mathbb{Q})$ and the compactly supported intersection cohomology groups $IH^{i}_{c}(X, \mathbb{Q})$ have mixed Hodge structures. We compare these two mixed Hodge structures for varieties with pre-$k$-rational singularities. We then study various notions of differential forms on varieties with pre-$k$-rational singularities. In particular, we investigate the depth of the complex $\underline{\Omega}^{p}_{X}$, where $\underline{\Omega}^{p}_{X}$ is the $p^{th}$-graded piece of the Du Bois complex.

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Scott Hiatt. 2025-09-04. Differential forms on varieties with pre-$k$-rational singularities. https://arxiv.org/abs/2509.04382

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