Rees algebras of sparse determinantal ideals

TY - JOUR

T1 - Rees algebras of sparse determinantal ideals

AU - Celikbas, Ela

AU - Dufresne, Emilie

AU - Fouli, Louiza

AU - Gorla, Elisa

AU - Lin, Kuei-Nuan

AU - Polini, Claudia

AU - Swanson, Irena

N1 - © 2024 American Mathematical Society. This is an author-produced version of the published paper. Uploaded in accordance with the publisher’s self-archiving policy. Further copying may not be permitted; contact the publisher for details.

PY - 2024/2/14

Y1 - 2024/2/14

N2 - We determine the defining equations of the Rees algebra and of the special fiber ring of the ideal of maximal minors of a $2\times n$ sparse matrix. We prove that their initial algebras are ladder determinantal rings. This allows us to show that the Rees algebra and the special fiber ring are Cohen-Macaulay domains, they are Koszul, they have rational singularities in characteristic zero and are F-rational in positive characteristic.

AB - We determine the defining equations of the Rees algebra and of the special fiber ring of the ideal of maximal minors of a $2\times n$ sparse matrix. We prove that their initial algebras are ladder determinantal rings. This allows us to show that the Rees algebra and the special fiber ring are Cohen-Macaulay domains, they are Koszul, they have rational singularities in characteristic zero and are F-rational in positive characteristic.

KW - math.AC

KW - Primary 13A30, 13C40, Secondary 14M12, 13P10, 05E40, 13F50

U2 - 10.1090/tran/9101

DO - 10.1090/tran/9101

M3 - Article

SN - 0002-9947

VL - 377

SP - 2317

EP - 2333

JO - Transactions of the American Mathematical Society

JF - Transactions of the American Mathematical Society

ER -