An explicit Koppelman formula for $dd^c$ and Green currents on $\mathcal P^n$

TL;DR

This paper derives an explicit Koppelman formula for the operator dd^c on projective space, enabling the construction of Green currents for positive closed currents, which advances the understanding of complex differential operators on projective varieties.

Contribution

It provides a new explicit Koppelman formula for dd^c on projective space and constructs Green currents for positive closed currents, enhancing tools in complex geometry.

Findings

Explicit Koppelman formula for dd^c on projective space

Construction of Green currents for positive closed currents

Improved methods for complex differential operators

Abstract

We compute a quite explicit Koppelman formula for $dd^c$ on projective space, and obtain Green currents for positive closed currents.