%0 Journal Article %1 aprodu2024reducedresonanceschemeschen %A Aprodu, Marian %A Farkas, Gavril %A Raicu, Claudiu %A Suciu, Alexander I. %D 2024 %J Journal für die Reine und Angewandte Mathematik (Crelle's Journal) %K %R 10.1515/crelle-2024-0051 %T Reduced resonance schemes and Chen ranks %U https://arxiv.org/abs/2303.07855 %X 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 Kähler and right-angled Artin groups.

@article{aprodu2024reducedresonanceschemeschen, 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 Kähler and right-angled Artin groups.}, added-at = {2024-07-23T01:47:14.000+0200}, archiveprefix = {arXiv}, author = {Aprodu, Marian and Farkas, Gavril and Raicu, Claudiu and Suciu, Alexander I.}, biburl = {https://www.bibsonomy.org/bibtex/242636f32a5f08eb7c6c491d2a92cc026/asuciu}, doi = {10.1515/crelle-2024-0051}, eprint = {2303.07855}, interhash = {279c6983ab29dc73a93eab95611cb539}, intrahash = {42636f32a5f08eb7c6c491d2a92cc026}, journal = {Journal für die Reine und Angewandte Mathematik (Crelle's Journal)}, keywords = {}, month = {july}, primaryclass = {math.AG}, timestamp = {2024-07-23T01:47:14.000+0200}, title = {Reduced resonance schemes and Chen ranks}, url = {https://arxiv.org/abs/2303.07855}, year = 2024 }