Reduced resonance schemes and Chen ranks
Algebraic Geometry
2024-09-16 v2 Algebraic Topology
Abstract
The resonance varieties are cohomological invariants that are studied in a variety of topological, combinatorial, and geometric contexts. We discuss their scheme structure in a general algebraic setting and introduce various properties that ensure the reducedness of the associated projective resonance scheme. We prove an asymptotic formula for the Hilbert series of the associated Koszul module, then discuss applications to vector bundles on algebraic curves and to Chen ranks formulas for finitely generated groups, with special emphasis on K\"ahler and right-angled Artin groups.
Keywords
Cite
@article{arxiv.2303.07855,
title = {Reduced resonance schemes and Chen ranks},
author = {Marian Aprodu and Gavril Farkas and Claudiu Raicu and Alexander I. Suciu},
journal= {arXiv preprint arXiv:2303.07855},
year = {2024}
}
Comments
36 pages. Final version, to appear in the Journal fuer die reine und angewandte Mathematik (Crelle)