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arXiv · 2604.05553

Minimal-Degree Foliations on Cominuscule Grassmannians

Vladimiro Benedetti·Crislaine Kuster·Alan Muniz
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Abstract

Given $X$ a cominuscule Grassmannian (or irreducible Hermitian symmetric space) and an integer $p,$ we compute the minimum $l(p)$ such that $H^0 (\Omega^p_X (l(p)))$ is not 0. This allows us to conclude that any codimension-one foliation of degree zero on a cominuscule Grassmannian is a pencil of hyperplanes, improving a result of the first and third authors with D. Faenzi. We also deduce the structure of codimension-one foliations of degree one. Finally, we provide families of examples of high codimensional foliations of minimal degree on classical Grassmannians, Lagrangian Grassmannians, Spinor varieties, and the Cayley plane.

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Vladimiro Benedetti, Crislaine Kuster, Alan Muniz. 2026-04-07. Minimal-Degree Foliations on Cominuscule Grassmannians. https://arxiv.org/abs/2604.05553

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