Alan Muniz (Université de Bourgogne) : Foliations on homogeneous spaces

A codimension-1 foliation on a projective manifold X can be thought of as a corank-1 saturated subsheaf F of the tangent bundle TX which is stable under the Lie bracket. After fixing the determinant of F, the set of such foliations is a locally closed subset of the space of 1-forms on X with values in some fixed line bundle L. We investigate the set of these foliations when X is a projective homogeneous space of Picard rank 1, for the simplest possible choice of L. A special focus will be on Grassmannians, most notably Grassmannians of lines, where our foliations are particularly easy to describe. This is based on arXiv:2209.06487, joint with V. Benedetti and D. Faenzi.