arXiv subjects

Federico Bongiorno

Publications and source records attributed to Federico Bongiorno.

5 recordsLinked to original sources

arXiv2026

Singularities of Foliations and Good Moduli Spaces of Algebraic Stacks

Drawing on the theory of Minimal Model Program singularities for foliations, we define relative canonical and log-canonical singularities for algebraic stacks with finite generic stabilisers. We show that if a point has log-canonical singularities, its stabiliser group is a finite extension of an algebraic torus, thus, étale locally, the good moduli space exists. If the singularity is canonical, we further show that the locus of stable points is non-empty.

math.AG↗

arXiv2025

Regular Leaves of Singular Foliations

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.

math.AG↗

arXiv2024

A Frobenius theorem in algebraic geometry

We show that a formal Deligne--Mumford stack is formal-locally represented by a formal scheme. This is an analogue of Frobenius theorem for smooth foliations in any characteristic and without smoothness hypotheses on the ambient space.

math.AG↗

arXiv2024

Formal schemes and infinitesimal neighbourhoods

The aim of this article is to give a rigorous geometric interpretation of the completion of a ring with respect to an ideal. To this end, we define the infinitesimal neighbourhood of an immersion of formal schemes as the largest possible thickening. Further, we show that immersions of formal schemes locally of formal finite presentation admit the existence of infinitesimal neighbourhoods, which are locally given by completing with respect to an ideal.

math.AG↗

arXiv2021

On the construction of quotient spaces by algebraic foliations

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.

math.AG↗