Split distributions on Grassmann manifolds and smooth quadric hypersurfaces
Alana Cavalcante, Fernando Lourenço
Published: 2025/5/7
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.