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arXiv · 1703.01861

The $\bar{\partial}$-equation on a non-reduced analytic space

Mats Andersson·Richard Lärkäng
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Abstract

Let $X$ be a, possibly non-reduced, analytic space of pure dimension. We introduce a notion of $\overline{\partial}$-equation on $X$ and prove a Dolbeault-Grothendieck lemma. We obtain fine sheaves $\mathcal{A}_X^q$ of $(0,q)$-currents, so that the associated Dolbeault complex yields a resolution of the structure sheaf $\mathscr{O}_X$. Our construction is based on intrinsic semi-global Koppelman formulas on $X$.

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Mats Andersson, Richard Lärkäng. 2017-03-06. The $\bar{\partial}$-equation on a non-reduced analytic space. https://doi.org/10.1007/s00208-018-1678-8

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