The article refines and generalises the study of deformations of a morphism along a foliation begun by Y. Miyaoka, [Mi2]. The key ingredients are the algebrisation of the graphic neighbourhood, see Fact 3.3.1, which reduces the problem from the transcendental to the algebraic, and a p-adic variation of Mori's bend and break in order to overcome the ``naive failure'', see Remark 3.2.3, of the method in the required generality. Qualitatively the results are optimal for foliations of all ranks in all dimensions, and are quantitatively optimal for foliations by curves, for which the further precision of a cone theorem is provided.
Bogomolov, ., Mcquillan, M., Michael, (2016). Rational Curves on Foliated Varieties. In P.M. Cascini (a cura di), Foliation Theory in Algebraic Geometry (pp. 21-51). Cham : Springer International Publishing [10.1007/978-3-319-24460-0_2].
Rational Curves on Foliated Varieties
MCQUILLAN, MICHAEL;
2016-01-01
Abstract
The article refines and generalises the study of deformations of a morphism along a foliation begun by Y. Miyaoka, [Mi2]. The key ingredients are the algebrisation of the graphic neighbourhood, see Fact 3.3.1, which reduces the problem from the transcendental to the algebraic, and a p-adic variation of Mori's bend and break in order to overcome the ``naive failure'', see Remark 3.2.3, of the method in the required generality. Qualitatively the results are optimal for foliations of all ranks in all dimensions, and are quantitatively optimal for foliations by curves, for which the further precision of a cone theorem is provided.| File | Dimensione | Formato | |
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