We provide several applications of the minimal model program to the local and global study of co-rank 1 foliations on threefolds. Locally, we prove a singular variant of Malgrange's theorem, a classification of terminal foliation singularities and the existence of separatrices for log canonical singularities. Globally, we prove termination of flips, a connectedness theorem on log canonical centres, a non-vanishing theorem and some hyperbolicity properties of foliations.

Local and global applications of the Minimal Model Program for co-rank 1 foliations on threefolds / C. Spicer, R. Svaldi. - In: JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY. - ISSN 1435-9855. - 24:11(2022), pp. 3969-4025. [10.4171/JEMS/1173]

Local and global applications of the Minimal Model Program for co-rank 1 foliations on threefolds

R. Svaldi
Ultimo
2022

Abstract

We provide several applications of the minimal model program to the local and global study of co-rank 1 foliations on threefolds. Locally, we prove a singular variant of Malgrange's theorem, a classification of terminal foliation singularities and the existence of separatrices for log canonical singularities. Globally, we prove termination of flips, a connectedness theorem on log canonical centres, a non-vanishing theorem and some hyperbolicity properties of foliations.
Foliations; minimal model program; singularities; separatrices; hyperbolicity
Settore MAT/03 - Geometria
2022
2021
https://ems.press/journals/jems/articles/3731347
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/937286
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