Parseval-Rayleigh identities for homogeneous complete intersections
Karim Alexander Adiprasito, Ryoshun Oba, Stavros Argyrios Papadakis, Vasiliki Petrotou
TL;DR
This paper establishes Parseval-Rayleigh identities for residue maps in homogeneous complete intersections over any positive characteristic, and uses this to prove the Strong Lefschetz Property for generic cases in characteristic 2.
Contribution
It introduces Parseval-Rayleigh identities in positive characteristic and provides a new proof of the Strong Lefschetz Property for generic homogeneous complete intersections in characteristic 2.
Findings
Parseval-Rayleigh identities hold in positive characteristic.
Generic homogeneous complete intersections have the Strong Lefschetz Property in characteristic 2.
Provides a conceptual proof for a folklore fact.
Abstract
We prove, in any positive characteristic, Parseval-Rayleigh identities for the residue map of a homogeneous complete intersection. As an application, we give a conceptual proof of the folklore fact that generic homogeneous complete intersections have the Strong Lefschetz Property over any field of characteristic 2.
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
TopicsAlgebraic Geometry and Number Theory · Commutative Algebra and Its Applications · Polynomial and algebraic computation