Koszul Determinantal Rings and 2 x e Matrices of Linear Forms

Autor(en): Nguyen, Hop D.
Phong Dinh Thieu
Thanh Vu
Stichwörter: ALGEBRAS; CANONICAL FORM; COMPUTATION; IDEAL; Mathematics; PROPERTY; RESOLUTION; SINGULAR PENCIL
Erscheinungsdatum: 2015
Herausgeber: MICHIGAN MATHEMATICAL JOURNAL
Journal: MICHIGAN MATHEMATICAL JOURNAL
Volumen: 64
Ausgabe: 2
Startseite: 349
Seitenende: 381
Zusammenfassung: 
Let k be an algebraically closed field of characteristic 0. Let X be a 2 x e matrix of linear forms over a polynomial ring k[x(1), ..., x(n)] (where e,n >= 1). We prove that the determinantal ring R = k[x(1), ..., x(n)]/I-2(X) is Koszul if and only if in any Kronecker-Weierstrass normal form of X, the largest length of a nilpotent block is at most twice the smallest length of a scroll block. As an application, we classify rational normal scrolls whose all section rings by natural coordinates are Koszul. This result settles a conjecture of Conca.
ISSN: 00262285
DOI: 10.1307/mmj/1434731928

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