Schmidt Rank and Singularities

David Kazhdan, Amichai Lampert, Alexander Polishchuk*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

We revisit Schmidt’s theorem connecting the Schmidt rank of a tensor with the codimension of a certain variety and adapt the proof to the case of arbitrary characteristic. We also establish a sharper result for this kind for homogeneous polynomials, assuming that the characteristic does not divide the degree. Further, we use this to relate the Schmidt rank of a homogeneous polynomial (resp., a collection of homogeneous polynomials of the same degree) with the codimension of the singular locus of the corresponding hypersurface (resp., intersection of hypersurfaces). This gives an effective version of Ananyan–Hochster’s theorem [J. Amer. Math. Soc., 33, No. 1, 291–309 (2020), Theorem A].

Original languageEnglish
Pages (from-to)1420-1442
Number of pages23
JournalUkrainian Mathematical Journal
Volume75
Issue number9
DOIs
StatePublished - Feb 2024

Bibliographical note

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© Springer Science+Business Media, LLC, part of Springer Nature 2024.

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