D-module structure of local cohomology modules of toric algebras

2010/05/11 by Jen-Chieh Hsiao, Hsiao, Jen-Chieh
Mathematics · #13D45 #13N10 #14M25 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.1005.1972

openalex publication_date 2010/05/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let S be a toric algebra over a field K of characteristic 0 and let I be a monomial ideal of S. We show that the local cohomology modules Hⁱ_I(S) are of finite length over the ring of differential operators D(S;K), generalizing the classical case of a polynomial algebra S. As an application, we compute the characteristic cycles of some local cohomology modules.

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