Grassmann 簇子簇的余法秩
Conormal Rank of Subvarieties of Grassmannians
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中文总结 AI 辅助
本文在 Grassmann 簇子簇上定义余法秩，证明低余法秩超曲面为 Chow–Lam 形式推广，并计算 Schubert 簇等族的余法秩。
中文摘要 AI 辅助
Grassmann 簇的任何子簇的余切空间自然等同于一个线性同态空间。我们利用这一点，在 Grassmann 簇的子簇上定义了一个新的统计量，称为“余法秩”。我们证明 Chow–Lam 形式及其自然推广具有低余法秩，并且进一步地，足够低余法秩的超曲面都具有这种形式，从而推广了 Gelfand–Kapranov–Zelevinsky 的一个结果。我们还计算了许多簇族的余法秩，包括 Schubert 簇、环面轨道闭包和 positroid 簇。
英文摘要
The cotangent space to any subvariety of a Grassmannian is naturally identified with a space of linear homomorphisms. We use this to define a new statistic on a subvariety of a Grassmannian, called \emph{conormal rank}. We show that Chow--Lam forms and their natural generalizations have low conormal rank, and moreover that hypersurfaces of sufficiently low conormal rank are all of this form, generalizing a result of Gelfand--Kapranov--Zelevinsky. We also compute the conormal rank of many families of varieties, including Schubert varieties, torus orbit closures, and positroid varieties.
