Reduced resonance schemes and Chen ranks-Reference-Cited by-同舟云学术

Reduced resonance schemes and Chen ranks

Published:2024-07-23 Issue: Volume: Page:
ISSN:0075-4102
Container-title:Journal für die reine und angewandte Mathematik (Crelles Journal)
language:en
Short-container-title:

Author:

Aprodu Marian¹,Farkas Gavril²,Raicu Claudiu³,Suciu Alexander I.⁴^ORCID

Affiliation:

1. Simion Stoilow Institute of Mathematics , P. O. Box 1-764, RO-014700; and Faculty of Mathematics and Computer Science, University of Bucharest , Bucharest , Romania

2. Institut für Mathematik , Humboldt-Universität zu Berlin , Unter den Linden 6, 10099 Berlin , Germany

3. Department of Mathematics , University of Notre Dame , 255 Hurley , Notre Dame , IN 46556 , USA ; and Simion Stoilow Institute of Mathematics, P. O. Box 1-764, RO-014700, Bucharest, Romania

4. Department of Mathematics , Northeastern University , Boston , MA 02115 , USA

Abstract

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.

Funder

Ministerul Cercetării şi Inovării

Deutsche Forschungsgemeinschaft

European Research Council

National Science Foundation

Simons Foundation

H2020 European Research Council

Publisher

Walter de Gruyter GmbH

Link

https://www.degruyter.com/document/doi/10.1515/crelle-2024-0051/pdf

Reference45 articles.

1. M. Aprodu, G. Farkas, Ş. Papadima, C. Raicu and J. Weyman, Koszul modules and Green’s conjecture, Invent. Math. 218 (2019), no. 3, 657–720.

2. M. Aprodu, G. Farkas, Ş. Papadima, C. Raicu and J. Weyman, Topological invariants of groups and Koszul modules, Duke Math. J. 171 (2022), no. 10, 2013–2046.

3. M. Aprodu, G. Farkas, C. Raicu, A. Sammartano and A. I. Suciu, Higher resonance schemes and Koszul modules of simplicial complexes, J. Algebraic Combin. 59 (2024), no. 4, 787–805.

4. M. Aprodu, G. Farkas, C. Raicu and A. I. Suciu, The effective Chen rank conjecture, work in progress.

5. M. Aprodu, G. Farkas, C. Raicu and J. Weyman, Koszul modules with vanishing resonance in algebraic geometry, Selecta Math. (N. S.) 30 (2024), no. 2, Paper No. 24.

Cited by 1 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. Milnor fibrations of arrangements with trivial algebraic monodromy;Revue Roumaine Mathematiques Pures Appliquees;2024-06-30