We prove the case t = 2 of a conjecture of Bruns–Conca– Varbaro, describing the minimal relations between the t × t minors of a generic matrix. Interpreting these relations as polynomial functors, and applying transpose duality as in the work of Sam–Snowden, this problem is equivalent to understanding the relations satisfied by t × t generalized permanents. Our proof follows by combining Koszul homology calculations on the minors side, with a study of subspace varieties on the permanents side, and with the Kempf– Weyman technique (on both sides).

Relations between the 2x2 minors of a generic matrix

A. Sammartano
2021-01-01

Abstract

We prove the case t = 2 of a conjecture of Bruns–Conca– Varbaro, describing the minimal relations between the t × t minors of a generic matrix. Interpreting these relations as polynomial functors, and applying transpose duality as in the work of Sam–Snowden, this problem is equivalent to understanding the relations satisfied by t × t generalized permanents. Our proof follows by combining Koszul homology calculations on the minors side, with a study of subspace varieties on the permanents side, and with the Kempf– Weyman technique (on both sides).
2021
Determinantal varieties
Koszul homology
Relations between minors
Grassmannian
File in questo prodotto:
File Dimensione Formato  
relns2x2minors.pdf

Open Access dal 07/08/2023

: Post-Print (DRAFT o Author’s Accepted Manuscript-AAM)
Dimensione 394.93 kB
Formato Adobe PDF
394.93 kB Adobe PDF Visualizza/Apri
Relations between the 2 × 2 minors of a generic matrix AiM.pdf

Accesso riservato

: Publisher’s version
Dimensione 495.9 kB
Formato Adobe PDF
495.9 kB Adobe PDF   Visualizza/Apri

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11311/1192333
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 4
  • ???jsp.display-item.citation.isi??? 2
social impact