PreprintCC BY 4.0HAL
Minimal-Degree Foliations on Cominuscule Grassmannians
Abstract
Let X be a cominuscule Grassmannian (equivalently, an irreducible Hermitian symmetric space), and let p be an integer. We compute the minimum l(p) such that H0(ΩXp(l(p))) ≠ 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.
Related
- CMC foliations on Euclidean spaces are minimal foliations
- Structural stability of the Jouanolou foliations in every degree
- A min-max gap characterization of minimal foliations on the torus
- Stability of Diophantine Minimal Foliations in Arbitrary Codimension
- Minimal foliations, codimension-one stable norms, and a question of Bangert
BibTeX
@misc{benedetti2026minimaldegree,
title = {{Minimal-Degree Foliations on Cominuscule Grassmannians}},
author = {Vladimiro Benedetti and Crislaine Kuster and Alan Muniz},
howpublished = {HAL},
year = {2026},
month = sep,
eprint = {2604.05553},
archivePrefix = {arXiv},
url = {https://hal.science/hal-05580248v3},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Minimal-Degree Foliations on Cominuscule Grassmannians
AU - Vladimiro Benedetti
AU - Crislaine Kuster
AU - Alan Muniz
PY - 2026
DA - 2026/09/11
PB - HAL
UR - https://hal.science/hal-05580248v3
AB - Let X be a cominuscule Grassmannian (equivalently, an irreducible Hermitian symmetric space), and let p be an integer. We compute the minimum l(p) such that H^0(Ω_X^p(l(p))) ≠ 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.
ER -