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arXiv · 2609.24694

Conormal Rank of Subvarieties of Grassmannians

Elizabeth Pratt
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Abstract

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.

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Elizabeth Pratt. 2026-09-21. Conormal Rank of Subvarieties of Grassmannians. https://arxiv.org/abs/2609.24694

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