Regular Leaves of Singular Foliations

2025/10/23 by Bongiorno, Federico
#Algebraic Geometry (math.AG) #Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.2510.20760

Abstract

We identify a class of singular algebraic foliations whose leaves through singular points retain regularity. The proof consists in showing existence of residual gerbes for certain formal stacks, which do not enjoy smooth presentations. As applications, we extend a theorem of Cerveau to the case where the ambient scheme is not smooth and we give a proof of the Zariski--Lipman conjecture for varieties with terminal singularities, which does not rely on existence of resolution of singularities.

Citations

• Resolution of 1-foliations singularities on surfaces and threefolds
• A Frobenius theorem in algebraic geometry
• Formal schemes and infinitesimal neighbourhoods
• Infinitesimal derived foliations
• MMP for co-rank one foliations on threefolds
• The Zariski-Lipman conjecture for log canonical spaces
• Local structure theorems for smooth maps of formal schemes
• Infinitesimal lifting and Jacobi criterion for smoothness on formal schemes
• Generalized Divisors and Biliaison

Related

• Resolution of 1-foliations singularities on surfaces and threefolds
• Codimension 1 foliations with numerically trivial canonical class on singular spaces
• Bounds on leaves of foliations of the plane
• Singular foliations through diffeology
• Singular Riemannian Foliations: Exceptional Leaves; Tautness