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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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Cite

BibTeXRIS
BibTeX
@misc{pratt2026conormal,
  title = {{Conormal Rank of Subvarieties of Grassmannians}},
  author = {Elizabeth Pratt},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.24694},
  eprint = {2609.24694},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.24694},
}
RIS
TY  - UNPB
TI  - Conormal Rank of Subvarieties of Grassmannians
AU  - Elizabeth Pratt
PY  - 2026
DA  - 2026/09/21
PB  - arXiv
DO  - 10.48550/arxiv.2609.24694
UR  - https://arxiv.org/abs/2609.24694
AB  - 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.
ER  -