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Bibliographic Details
Main Authors: Johansson, Jimmy, Lärkäng, Richard
Format: Preprint
Published: 2021
Subjects:
Online Access:https://arxiv.org/abs/2109.00480
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Table of 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 $\mathcal{F}$.