Translator Disclaimer
2020 Iterated local cohomology groups and Lyubeznik numbers for determinantal rings
András C. Lőrincz, Claudiu Raicu
Algebra Number Theory 14(9): 2533-2569 (2020). DOI: 10.2140/ant.2020.14.2533

Abstract

We give an explicit recipe for determining iterated local cohomology groups with support in ideals of minors of a generic matrix in characteristic zero, expressing them as direct sums of indecomposable 𝒟-modules. For nonsquare matrices these indecomposables are simple, but this is no longer true for square matrices where the relevant indecomposables arise from the pole order filtration associated with the determinant hypersurface. Specializing our results to a single iteration, we determine the Lyubeznik numbers for all generic determinantal rings, thus answering a question of Hochster.

Citation

Download Citation

András C. Lőrincz. Claudiu Raicu. "Iterated local cohomology groups and Lyubeznik numbers for determinantal rings." Algebra Number Theory 14 (9) 2533 - 2569, 2020. https://doi.org/10.2140/ant.2020.14.2533

Information

Received: 20 November 2019; Revised: 27 March 2020; Accepted: 29 April 2020; Published: 2020
First available in Project Euclid: 12 November 2020

MathSciNet: MR4172715
Digital Object Identifier: 10.2140/ant.2020.14.2533

Subjects:
Primary: 13D45
Secondary: 13D07, 14M12

Rights: Copyright © 2020 Mathematical Sciences Publishers

JOURNAL ARTICLE
37 PAGES

This article is only available to subscribers.
It is not available for individual sale.
+ SAVE TO MY LIBRARY

SHARE
Vol.14 • No. 9 • 2020
MSP
Back to Top