Vanishing Cycles in Holomorphic Foliations by Curves and Foliated Shells

TL;DR

This paper investigates vanishing cycles in holomorphic foliations on compact complex manifolds and introduces the concept of a foliated shell, a complex geometric structure associated with these cycles.

Contribution

It establishes a novel connection between vanishing cycles and foliated shells, enriching the understanding of complex geometric structures in holomorphic foliations.

Findings

Vanishing cycles are associated with foliated shells.

Foliated shells provide a richer geometric context for vanishing cycles.

The study advances the understanding of complex structures in holomorphic foliations.

Abstract

The purpose of this paper is the study of vanishing cycles in holomorphic foliations by complex curves on compact complex manifolds. The main result consists in showing that a vanishing cycle comes together with a much richer complex geometric object - we call this object a foliated shell.