Germs of integrable forms and varieties of minimal degree

TL;DR

This paper investigates the geometric properties of integrable 1-forms in a finite-dimensional space, revealing that certain irreducible components are characterized by minimal degree, which advances understanding of their algebraic structure.

Contribution

It establishes that irreducible components of integrable 1-forms with large dimension are of minimal degree, providing new insights into their geometric and algebraic properties.

Findings

Irreducible components with dimension comparable to the rank are of minimal degree.

The study characterizes the subvariety of integrable 1-forms within a finite-dimensional vector space.

Provides a geometric classification of integrable forms based on degree properties.

Abstract

We study the subvariety of integrable 1-forms in a finite dimensional vector space $W \subset \Omega^1(\mathbb C^n,0)$. We prove that the irreducible components with dimension comparable with the rank of $W$ are of minimal degree.