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arXiv · 2505.04724

Split distributions on Grassmann manifolds and smooth quadric hypersurfaces

Alana Cavalcante·Fernando Lourenço
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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.

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Alana Cavalcante, Fernando Lourenço. 2025-05-07. Split distributions on Grassmann manifolds and smooth quadric hypersurfaces. https://arxiv.org/abs/2505.04724

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