On the construction of quotient spaces by algebraic foliations

TL;DR

This paper proves the existence of a categorical quotient for algebraically integrable foliations of corank ≤ 2 on varieties over characteristic zero fields, ensuring a universal property for invariant morphisms.

Contribution

It establishes the existence of categorical quotients for certain algebraic foliations, extending the understanding of invariant structures in algebraic geometry.

Findings

Existence of categorical quotients for algebraically integrable foliations of corank ≤ 2

Universal property for invariant morphisms

Construction valid on the open set of stable points

Abstract

Given a variety defined over a field of characteristic zero and an algebraically integrable foliation of corank less than or equal to two, we show the existence of a categorical quotient, defined on the non-empty open set of stable points, through which every invariant morphism factors uniquely.