REES ALGEBRAS OF SPARSE DETERMINANTAL IDEALS

Ela Celikbas; Emilie Dufresne; Louiza Fouli; Elisa Gorla; Kuei Nuan Lin; Claudia Polini; Irena Swanson

doi:10.1090/tran/9101

REES ALGEBRAS OF SPARSE DETERMINANTAL IDEALS

Ela Celikbas, Emilie Dufresne, Louiza Fouli, Elisa Gorla, Kuei Nuan Lin, Claudia Polini, Irena Swanson

Penn State Greater Allegheny

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

We determine the defining equations of the Rees algebra and of the special fiber ring of the ideal of maximal minors of a 2 × 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.

Original language	English (US)
Pages (from-to)	2317-2333
Number of pages	17
Journal	Transactions of the American Mathematical Society
Volume	377
Issue number	4
DOIs	https://doi.org/10.1090/tran/9101
State	Published - Apr 2024

All Science Journal Classification (ASJC) codes

General Mathematics
Applied Mathematics

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10.1090/tran/9101

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abstract = "We determine the defining equations of the Rees algebra and of the special fiber ring of the ideal of maximal minors of a 2 × 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.",

author = "Ela Celikbas and Emilie Dufresne and Louiza Fouli and Elisa Gorla and Lin, {Kuei Nuan} and Claudia Polini and Irena Swanson",

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AU - Fouli, Louiza

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AU - Lin, Kuei Nuan

AU - Polini, Claudia

AU - Swanson, Irena

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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 × 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 × 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.

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ER -

REES ALGEBRAS OF SPARSE DETERMINANTAL IDEALS

Abstract

All Science Journal Classification (ASJC) codes

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