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Poincaré duality and resonance varieties

Part of: Basic linear algebra Applied homological algebra and category theory Special varieties Chain conditions, finiteness conditions General commutative ring theory Generalized manifolds Topological manifolds

Published online by Cambridge University Press:  13 September 2019

Alexander I. Suciu
Alexander I. Suciu*
Affiliation:
Department of Mathematics, Northeastern University, Boston, Massachusetts02115, USA ([email protected]) web.northeastern.edu/suciu/
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Abstract

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

Keywords

Graded commutative algebraresonance varietyPoincaré duality algebraconnected sumBGG correspondencealternating 3-formPfaffian

MSC classification

Primary: 55U30: Duality 57P10: Poincaré duality spaces
Secondary: 13A02: Graded rings 13E10: Artinian rings and modules, finite-dimensional algebras 14M12: Determinantal varieties 15A75: Exterior algebra, Grassmann algebras 57N10: Topology of general $3$-manifolds
Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 150 , Issue 6 , December 2020 , pp. 3001 - 3027
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Copyright
Copyright © 2019 The Royal Society of Edinburgh

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