Toric foliations with split tangent sheaf

TL;DR

This paper investigates holomorphic foliations on smooth complete toric varieties, demonstrating stability of split foliations under certain conditions and identifying irreducible components of the foliation space as pullbacks of specific invariant divisors.

Contribution

It introduces conditions for the stability of split foliations and characterizes certain irreducible components of the foliation space as pullbacks of T-invariant divisors.

Findings

Split foliations are stable under specific singular set conditions.

Irreducible components of the foliation space can be realized as pullbacks of T-invariant divisors.

Provides new insights into the structure of foliations on toric varieties.

Abstract

We study holomorphic foliations of aribitrary codimension in smooth complete toric varieties. We show that split foliations are stable if some good behaviour of their singular set is provided. As an application of these results, we exhibit irreducible components of the space of foliations that arise as pullbacks of some special T-invariant divisors.