Poincar\'e duality and resonance varieties

TL;DR

This paper investigates how Poincaré duality influences the structure of resonance varieties in graded algebras, providing a detailed geometric description for 3-dimensional cases.

Contribution

It offers a new geometric characterization of resonance varieties in 3-dimensional Poincaré duality algebras, advancing understanding of their algebraic and topological properties.

Findings

Geometric description of resonance varieties for 3D Poincaré duality algebras

Constraints of Poincaré duality on resonance varieties

Enhanced understanding of algebraic-topological relationships

Abstract

We explore the constraints imposed by Poincar\'e duality on the resonance varieties of a graded algebra. For a 3-dimensional Poincar\'e duality algebra $A$, we obtain a fairly precise geometric description of the resonance varieties $\mathcal{R}^i_k(A)$.