# Koppelman formulas on affine cones over smooth projective complete intersections Preprint, 2015

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 \dbar-operators acting on L^p-spaces of forms, including the case p=2 if the varieties have canonical singularities. We also prove that the A-forms introduced by Andersson-Samuelsson are C^\alpha for \alpha<1.

## Författare

#### Richard Lärkäng

Göteborgs universitet

Chalmers, Matematiska vetenskaper, Matematik

#### Fundament

Grundläggande vetenskaper

#### Ämneskategorier

Geometri

Matematisk analys