Bernstein, Sturmfels and Zelevinsky proved in 1993 that the maximal minors of a matrix of variables form a universal Gröbner basis. We present a very short proof of this result, along with a broad generalization to matrices with multihomogeneous structures. Our main tool is a rigidity statement for radical Borel-fixed ideals in multigraded polynomial rings.

Universal Gröbner Bases for Maximal Minors of Matrices of Linear Forms

CONCA, ALDO
2015-01-01

Abstract

Bernstein, Sturmfels and Zelevinsky proved in 1993 that the maximal minors of a matrix of variables form a universal Gröbner basis. We present a very short proof of this result, along with a broad generalization to matrices with multihomogeneous structures. Our main tool is a rigidity statement for radical Borel-fixed ideals in multigraded polynomial rings.
2015
978-3-319-20154-2
978-3-319-20155-9
File in questo prodotto:
File Dimensione Formato  
(2015) Conca - Universal Gröbner Bases for Maximal Minors of Matrices of Linear Form.pdf

accesso chiuso

Tipologia: Documento in versione editoriale
Dimensione 124.81 kB
Formato Adobe PDF
124.81 kB Adobe PDF   Visualizza/Apri   Richiedi una copia

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/11567/860701
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 0
  • ???jsp.display-item.citation.isi??? 0
social impact