Quasi-analytische Zerlegungen

TL;DR

This paper develops a theory of quasi-analytic decompositions of complex manifolds, linking them to singular holomorphic foliations, and explores their properties and interrelations.

Contribution

It introduces a new framework for quasi-analytic layers and connects them with existing holomorphic foliation theories by Baum and Bott.

Findings

Quasi-analytic layers form a natural decomposition of complex manifolds.

A correspondence between quasi-analytic decompositions and Baum-Bott foliations is established.

The theory enhances understanding of singular holomorphic foliations.

Abstract

The leaves in singular holomorphic foliation theory are examples of quasi-analytic layers. In the first part of our publication we are concerned with a theory of these subjects. A quasi-analytic decomposition of a complex manifold is a decomposition into pairwise disjoint connected quasi-analytic layers. These are holomorphic foliations in the sense of P. Stefan and K. Spallek. A very different but more usual conception of holomorphic foliations is develloped by P. Baum and R. Bott. It is based on holomorphic sheaf theory. In the second part we study the relation between quasi-analytic decompositions and singular holomorphic foliations in the sense of Baum and Bott.