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| Main Author: | |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2312.01245 |
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Table of Contents:
- Let $X$ be a normal complex variety and $π:\tilde X \to X$ a resolution of singularities. We show that the inclusion morphism $π_*Ω_{\tilde X}^p\hookrightarrow Ω_X^{[p]}$ is an isomorphism for $p < \mathrm{codim}_X(X_{\mathrm{sing}})$ when $X$ has du Bois singularities, giving an improvement on Flenner's criterion for arbitrary singularities. We also study the $k$-du Bois definition from the perspective of holomorphic extension and compare how different restrictions on $\mathscr H^0(\underline Ω_X^p)$ affect the singularities of $X$, where $\underlineΩ_X^p$ is the $p^{th}$-graded piece of the du Bois complex.