An explicit isomorphism of different representations of the Ext functor using residue currents
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2021
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| _version_ | 1866913598019731456 |
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| author | Johansson, Jimmy Lärkäng, Richard |
| author_facet | Johansson, Jimmy Lärkäng, Richard |
| contents | Let $\mathcal{F}$ be a coherent $\mathcal{O}_X$-module over a complex manifold $X$, and let $G$ be a vector bundle on $X$. We describe an explicit isomorphism between two different representations of the global $\DeclareMathOperator{\Ext}{Ext}\Ext$ groups $\DeclareMathOperator{\Ext}{Ext}\Ext^k(\mathcal{F},G)$. The first representation is given by the cohomology of a twisted complex in the sense of Toledo and Tong, and the second one is obtained from the Dolbeault complex associated with $G$. A key tool that we introduce for explicitly describing this isomorphism is a residue current associated with a twisted resolution of $\mathcal{F}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2109_00480 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | An explicit isomorphism of different representations of the Ext functor using residue currents Johansson, Jimmy Lärkäng, Richard Complex Variables 18G15, 32A27, 32C35 Let $\mathcal{F}$ be a coherent $\mathcal{O}_X$-module over a complex manifold $X$, and let $G$ be a vector bundle on $X$. We describe an explicit isomorphism between two different representations of the global $\DeclareMathOperator{\Ext}{Ext}\Ext$ groups $\DeclareMathOperator{\Ext}{Ext}\Ext^k(\mathcal{F},G)$. The first representation is given by the cohomology of a twisted complex in the sense of Toledo and Tong, and the second one is obtained from the Dolbeault complex associated with $G$. A key tool that we introduce for explicitly describing this isomorphism is a residue current associated with a twisted resolution of $\mathcal{F}$. |
| title | An explicit isomorphism of different representations of the Ext functor using residue currents |
| topic | Complex Variables 18G15, 32A27, 32C35 |
| url | https://arxiv.org/abs/2109.00480 |