Parseval-Rayleigh identities for homogeneous complete intersections

2025/11/07 by Adiprasito, Karim Alexander, Oba, Ryoshun, Papadakis, Stavros Argyrios +1
#13A35 #Commutative Algebra (math.AC) #FOS: Mathematics #Primary 13C40 #Secondary 14M10

paper · doi:10.48550/arxiv.2511.05288

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.

Citations

• Lattice polytopes and semigroup algebras: Generic Lefschetz properties and Parseval-Rayleigh identities
• The volume intrinsic to a commutative graded algebra
• On the anisotropy theorem of Papadakis and Petrotou
• The characteristic 2 anisotropicity of simplicial spheres
• Combinatorial Lefschetz theorems beyond positivity
• The Weak and Strong Lefschetz Properties for Artinian K-Algebras

Related

• The quadratic complete intersections with the action of the symmetric group
• Convex separably rationally connected complete intersections
• On Strong Lefschetz Property of 0-dimensional complete intersections and Veronese varieties
• Criteria for complete intersections
• The canonical strip phenomenon for complete intersections in homogeneous spaces