Koppelman formulas on affine cones over smooth projective complete intersections

Abstract

In the present paper, we study regularity of the Andersson-Samuelsson Koppelman integral operator on affine cones over smooth projective complete intersections. Particularly, we prove $L^p$- and $C^{\alpha }$-estimates, and compactness of the operator, when the degree is sufficiently small. As applications, we obtain homotopy formulas for different $\overline{\partial }$-operators acting on $L^p$-spaces of forms, including the case $p=2$ if the varieties have canonical singularities. We also prove that the $\mathcal{A}$-forms introduced by Andersson-Samuelsson are $C^{\alpha }$ for $\alpha <1$.

22 pages. v2: corrections from the review process. arXiv admin note: text overlap with arXiv:1407.5703

References in corpus (1)

• Koppelman formulas on the A_1-singularity

Cited by in corpus (5)

• Koppelman formulas on the A_1-singularity
• The $\bar{\partial }$-equation on a non-reduced analytic space
• Estimates for the $\bar{\partial }$-equation on canonical surfaces
• Norm estimates for the $\bar{\partial }$-equation on a non-reduced space
• Global Koppelman formulas on (singular) projective varieties