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Mathematics > Commutative Algebra

arXiv:1805.08895 (math)
[Submitted on 22 May 2018]

Title:Iterated local cohomology groups and Lyubeznik numbers for determinantal rings

Authors:András C. Lőrincz, Claudiu Raicu
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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 non-square 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.
Subjects: Commutative Algebra (math.AC); Algebraic Geometry (math.AG)
MSC classes: 13D07, 14M12, 13D45
Cite as: arXiv:1805.08895 [math.AC]
  (or arXiv:1805.08895v1 [math.AC] for this version)
  https://doi.org/10.48550/arXiv.1805.08895

Submission history

From: Claudiu Raicu [view email]
[v1] Tue, 22 May 2018 22:42:41 UTC (35 KB)
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