Norm estimates for the $\bar{\partial }$-equation on a non-reduced space

Abstract

We study norm-estimates for the $\bar{\partial }$-equation on non-reduced analytic spaces. Our main result is that on a non-reduced analytic space, which is Cohen-Macaulay and whose underlying reduced space is smooth, the $\bar{\partial }$-equation for $(0,1)$-forms can be solved with $L^p$-estimates.

28 pages