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arXiv · 1506.07842

The $\bar{\partial}$-equation, duality, and holomorphic forms on a reduced complex space

Håkan Samuelsson Kalm
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Abstract

We solve the $\bar{\partial}$-equation for $(p,q)$-forms locally on any reduced pure-dimensional complex space and we prove an explicit version of Serre duality by introducing suitable concrete fine sheaves of certain $(p,q)$-currents. In particular this gives a precise condition for the $\bar{\partial}$-equation to be globally solvable. Our results extend results for $(0,q)$-forms and give information about holomorphic $p$-forms on singular spaces.

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Håkan Samuelsson Kalm. 2015-06-25. The $\bar{\partial}$-equation, duality, and holomorphic forms on a reduced complex space. https://arxiv.org/abs/1506.07842

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