Canonical sheaves at isolated canonical Gorenstein singularities
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arXiv
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866912982824386560 |
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| author | Ruppenthal, Jean |
| author_facet | Ruppenthal, Jean |
| contents | It is well known that the Grauert-Riemenschneider canonical sheaf $\mathcal{K}_X$ of holomorphic square-integrable $n$-forms is a central tool in $L^2$-theory for the $\overline\partial$-operator on a singular complex space $X$ of pure dimension $n$. It was shown a few years ago that a comprehensive $L^2$-theory requires also the study of the sheaf $\mathcal{K}_X^s$ of holomorphic square-integrable $n$-forms with a Dirichlet boundary condition at the singular set of $X$. In the present paper, we describe and classify the behaviour of $\mathcal{K}_X^s$ in isolated canonical Gorenstein singularities, and give applications to the $L^2$-theory for the $\overline\partial$-operator on such spaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_24818 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Canonical sheaves at isolated canonical Gorenstein singularities Ruppenthal, Jean Complex Variables Algebraic Geometry 32J25, 32C35, 32W05 It is well known that the Grauert-Riemenschneider canonical sheaf $\mathcal{K}_X$ of holomorphic square-integrable $n$-forms is a central tool in $L^2$-theory for the $\overline\partial$-operator on a singular complex space $X$ of pure dimension $n$. It was shown a few years ago that a comprehensive $L^2$-theory requires also the study of the sheaf $\mathcal{K}_X^s$ of holomorphic square-integrable $n$-forms with a Dirichlet boundary condition at the singular set of $X$. In the present paper, we describe and classify the behaviour of $\mathcal{K}_X^s$ in isolated canonical Gorenstein singularities, and give applications to the $L^2$-theory for the $\overline\partial$-operator on such spaces. |
| title | Canonical sheaves at isolated canonical Gorenstein singularities |
| topic | Complex Variables Algebraic Geometry 32J25, 32C35, 32W05 |
| url | https://arxiv.org/abs/2603.24818 |