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The minimality of determinantal varieties

  • Martin Bordemann , Jaigyoung Choe EMAIL logo and Jens Hoppe
Published/Copyright: December 15, 2020

Abstract

The determinantal variety Σ p q is defined to be the set of all p × q real matrices with p q whose ranks are strictly smaller than q. It is proved that Σ p q is a minimal cone in p q and all its strata are regular minimal submanifolds.

Funding statement: Jaigyoung Choe was supported in part by NRF-2018R1A2B6004262.

Acknowledgements

Jaigyoung Choe would like to thank the Chinese University of Hong Kong Mathematics Department for their invitation in Spring 2019. Jens Hoppe would like to thank Teoman Turgut for valuable discussions.

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Received: 2020-03-20
Revised: 2020-10-01
Published Online: 2020-12-15
Published in Print: 2021-04-01

© 2020 Walter de Gruyter GmbH, Berlin/Boston

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