Split distributions on Grassmann manifolds and smooth quadric hypersurfaces

Abstract

This work is dedicated to studying holomorphic distributions on Grassmann manifolds and smooth quadric hypersurfaces. In special, we prove, under certain conditions, when the tangent and conormal sheaves of a distribution splits as a sum of line bundles on these manifolds, generalizing the previous works on Fano threefolds and $\mathbb{P}^{n}$. We analyze how the algebro-geometric properties of the singular set of singular holomorphic distributions relate to their associated sheaves.