A long exact sequence for homology of FI-modules

2016/02/29 by Wee Liang Gan, Gan, Wee Liang · 2 citations
Computer Science · Mathematics · #Algebraic structures and combinatorial models #Commutative Algebra and Its Applications #FOS: Mathematics #Representation Theory (math.RT) #Topological and Geometric Data Analysis

paper · pdf · doi:10.48550/arxiv.1602.08873

openalex publication_date 2016/02/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We construct a long exact sequence involving the homology of an FI-module. Using the long exact sequence, we give two methods to bound the Castelnuovo-Mumford regularity of an FI-module which is generated and related in finite degree. We also prove that for an FI-module which is generated and related in finite degree, if it has a nonzero higher homology, then its homological degrees are strictly increasing (starting from the first homological degree).

Citations

• A remark on FI-module homology

Cited by

• Bounds on homological invariants of VI-modules
• Two homological proofs of the Noetherianity of FI_G

Related

• A remark on FI-module homology
• Bounding the homology of FI-modules
• Homological Invariants of FI-modules and FI_G-modules
• Upper bounds of homological invariants of FI_G-modules
• Filtrations and Homological degrees of FI-modules