Local and global applications of the Minimal Model Program for co-rank 1 foliations on threefolds
Calum Spicer
King’s College London, UKRoberto Svaldi
Ecole Polytechnique Fédérale de Lausanne, Switzerland
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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.
Cite this article
Calum Spicer, Roberto Svaldi, Local and global applications of the Minimal Model Program for co-rank 1 foliations on threefolds. J. Eur. Math. Soc. 24 (2022), no. 11, pp. 3969–4025
DOI 10.4171/JEMS/1173