Foliations with positive slopes and birational stability of orbifold cotangent bundles
By Frédéric Campana, Mihai Paun. Publications mathématiques (Bures-sur-Yvette), 2015
134 citations recorded by the source corpus.
Let X\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$X$\end{document} be a smooth connected projective manifold, together with an snc orbifold divisor Δ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\Delta $\end{document}, such that the pair (X,Δ)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$(X, \Delta )$\end{document} is log-canonical. If KX+Δ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$K_{X}+\Delta $\end{document} is pseudo-effective, we show, among other things, that any quotient of its orbifold cotangent bundle has a pseudo-effective determinant. This improves considerably our previous result (Campana and Păun in Ann. Inst. Fourier. 65:835, 2015), where generic positivity instead of pseudo-effectivity was obtained. One of the new ingredients in the proof is a version of the Bogomolov-McQuillan algebraicity criterion for holomorphic foliations whose minimal slope with respect to a movable class (instead of an ample complete intersection class) is positive.
Subfields: Applied Mathematics, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/760e8376e1bdd87904f23d9fc5bc9484c109cc0b
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In Applied Mathematics
In Geometry and Topology
Citations in the corpus
- A decomposition theorem for singular spaces with trivial canonical class of dimension at most five (2016, methodology): “The geometric counterpart of Bost’s arithmetic algebraicity criterion, independently obtained by Bogomolov and McQuillan ([BM01]), and very recently extended by Campana and P˘aun ([CP15]) leads to the following algebraicity criterion.”