The characteristic variety of a generic foliation

TL;DR

This paper proves a conjecture that the characteristic variety of a generic polynomial vector field contains only trivial involutive subvarieties, confirming a specific prediction about its geometric structure.

Contribution

It confirms a conjecture by Bernstein-Lunts regarding the structure of characteristic varieties for generic polynomial vector fields.

Findings

Characteristic variety has no nontrivial homogeneous involutive subvarieties.

The zero section and fiber subvarieties over singular points are the only involutive subvarieties.

Supports the conjecture for generic polynomial vector fields.

Abstract

We confirm a conjecture of Bernstein-Lunts which predicts that the characteristic variety of a generic polynomial vector field has no homogeneous involutive subvarieties besides the zero section and subvarieties of fibers over singular points.