The canonical trace of determinantal rings

Antonino Ficarra; Jürgen Herzog; Dumitru I. Stamate; Vijaylaxmi Trivedi

doi:10.1007/s00013-024-02047-0

The canonical trace of determinantal rings

Antonino Ficarra
, Jürgen Herzog
, Dumitru I. Stamate
, Vijaylaxmi Trivedi

Mathematics

University of Messina
University of Duisburg-Essen
University of Bucharest

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

4 Scopus citations

Abstract

We compute the canonical trace of generic determinantal rings and provide a sufficient condition for the trace to specialize. As an application, we determine the canonical trace tr(ω_R) of a Cohen–Macaulay ring R of codimension two, which is generically Gorenstein. It is shown that if the defining ideal I of R is generated by n elements, then tr(ω_R) is generated by the (n-2)-minors of the Hilbert–Burch matrix of I.

Original language	English
Pages (from-to)	487-497
Number of pages	11
Journal	Archiv der Mathematik
Volume	123
Issue number	5
DOIs	https://doi.org/10.1007/s00013-024-02047-0
State	Published - Nov 2024

Keywords

Canonical traces
Determinantal rings
Perfect codimension 2 ideals
Primary 13H10
Secondary 13M05
Teter numbers

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10.1007/s00013-024-02047-0

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abstract = "We compute the canonical trace of generic determinantal rings and provide a sufficient condition for the trace to specialize. As an application, we determine the canonical trace tr(ωR) of a Cohen–Macaulay ring R of codimension two, which is generically Gorenstein. It is shown that if the defining ideal I of R is generated by n elements, then tr(ωR) is generated by the (n-2)-minors of the Hilbert–Burch matrix of I.",

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T1 - The canonical trace of determinantal rings

AU - Ficarra, Antonino

AU - Herzog, Jürgen

AU - Stamate, Dumitru I.

AU - Trivedi, Vijaylaxmi

N1 - Publisher Copyright: © Springer Nature Switzerland AG 2024.

PY - 2024/11

Y1 - 2024/11

N2 - We compute the canonical trace of generic determinantal rings and provide a sufficient condition for the trace to specialize. As an application, we determine the canonical trace tr(ωR) of a Cohen–Macaulay ring R of codimension two, which is generically Gorenstein. It is shown that if the defining ideal I of R is generated by n elements, then tr(ωR) is generated by the (n-2)-minors of the Hilbert–Burch matrix of I.

AB - We compute the canonical trace of generic determinantal rings and provide a sufficient condition for the trace to specialize. As an application, we determine the canonical trace tr(ωR) of a Cohen–Macaulay ring R of codimension two, which is generically Gorenstein. It is shown that if the defining ideal I of R is generated by n elements, then tr(ωR) is generated by the (n-2)-minors of the Hilbert–Burch matrix of I.

KW - Canonical traces

KW - Determinantal rings

KW - Perfect codimension 2 ideals

KW - Primary 13H10

KW - Secondary 13M05

KW - Teter numbers

UR - https://www.scopus.com/pages/publications/85204123082

U2 - 10.1007/s00013-024-02047-0

DO - 10.1007/s00013-024-02047-0

M3 - Article

AN - SCOPUS:85204123082

SN - 0003-889X

VL - 123

SP - 487

EP - 497

JO - Archiv der Mathematik

JF - Archiv der Mathematik

IS - 5

ER -

The canonical trace of determinantal rings

Abstract

Keywords

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