2024/11/06 by Pablo Perrella, Perrella, Pablo, Sebastián Velazquez +1
Agricultural and Biological Sciences · Engineering · #14D06 #14D15 #32M25 #32S65 #Algebraic Geometry (math.AG) #FOS: Mathematics #Plant Surface Properties and Treatments #Structural Analysis of Composite Materials
paper · pdf · doi:10.48550/arxiv.2411.04039
openalex publication_date 2024/11/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.