Work

Extendability of foliations

Year: 2025

Type: article

Abstract: Given a foliation F on X and an embedding X ⊆ Y , is there a foliation on Y extending F? Using formal methods, we show that this question has an affirmative answer whenever the embedding is sufficiently positive with respect to ( X , F ) and the singularities of F belong to a certain class. These tools also apply in the case where Y is the total space of a deformation of X. Regarding the uniqueness of the extension, we prove a foliated version of a statement by Fujita and Grauert ensuring the existence of tubular neighborhoods. We also give sufficient conditions for a foliation to have only trivial unfoldings, generalizing a result due to Gómez-Mont.

Source: Advances in Mathematics

DOI: 10.1016/j.aim.2025.110538

Authors: Pablo Perrella, Sebastián Velazquez

Institutions: Consejo Nacional de Investigaciones Científicas y Técnicas, Universidad de Buenos Aires, King's College London

Language: English

Topic: Algebraic Geometry and Number Theory

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,790

Funders: London Mathematical Society, Consejo Nacional de Investigaciones Científicas y Técnicas, Engineering and Physical Sciences Research Council