Codimension one foliations on homogeneous varieties

The aim of this paper is to study codimension one foliations on rational homogeneous spaces, with a focus on the moduli space of foliations of low degree on Grassmannians and cominuscule spaces. Using equivariant techniques, we show that codimension one degree zero foliations on (ordinary, orthogona...

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Bibliographic Details
Published in:Advances in mathematics (New York. 1965) 2023-12, Vol.434, p.109332, Article 109332
Main Authors: Benedetti, Vladimiro, Faenzi, Daniele, Muniz, Alan
Format: Article
Language:English
Subjects:
Algebraic Geometry
Codimension one foliations
Cominuscule Grassmannian
Differential Geometry
Distributions
Freudenthal's magic square
Mathematics
Moduli space of foliations
Rational homogeneous space
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Summary:The aim of this paper is to study codimension one foliations on rational homogeneous spaces, with a focus on the moduli space of foliations of low degree on Grassmannians and cominuscule spaces. Using equivariant techniques, we show that codimension one degree zero foliations on (ordinary, orthogonal, symplectic) Grassmannians of lines, some spinor varieties, some Lagrangian Grassmannians, the Cayley plane (an E6-variety) and the Freudenthal variety (an E7-variety) are identified with restrictions of foliations on the ambient projective space. We also provide some evidence that such results can be extended beyond these cases.
ISSN:0001-8708
1090-2082
DOI:10.1016/j.aim.2023.109332