De Rahm cohomology of local cohomology modules
Tony J. Puthenpurakal

TL;DR
This paper investigates the structure of local cohomology modules over polynomial rings in characteristic zero by computing their Koszul homology with respect to partial derivatives, revealing new insights into their algebraic properties.
Contribution
It computes the Koszul homology modules of local cohomology modules for specific classes of ideals, advancing understanding of their structure as holonomic modules.
Findings
Computed Koszul homology modules for certain ideals
Provided new structural insights into local cohomology modules
Extended previous results on holonomic modules
Abstract
Let be a field of characteristic zero, and let be an ideal in . Let be the Weyl algebra over . By a result due to Lyubeznik the local cohomology modules are holonomic -modules for each . In this article we compute the Koszul homology modules for certain classes of ideals.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsCommutative Algebra and Its Applications · Algebraic structures and combinatorial models · Advanced Combinatorial Mathematics
