Sklyanin algebras and Hilbert schemes of points

Nevins, T.A. and Stafford, J.T. (2006) Sklyanin algebras and Hilbert schemes of points. Advances in Mathematics, 210 (2). pp. 405-478. ISSN 0001-8708

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Abstract

We construct projective moduli spaces for torsion-free sheaves on noncommutative projective planes. These moduli spaces vary smoothly in the parameters describing the noncommutative plane and have good properties analogous to those of moduli spaces of sheaves over the usual (commutative) projective plane P^2. The generic noncommutative plane corresponds to the Sklyanin algebra S=Skl(E,σ) constructed from an automorphism σ of infinite order on an elliptic curve E ⊂ P^2. In this case, the fine moduli space of line bundles over S with first Chern class zero and Euler characteristic 1−n provides a symplectic variety that is a deformation of the Hilbert scheme of n points on P^2 \ E.

Item Type: Article
Uncontrolled Keywords: Moduli spaces; Hilbert schemes; Noncommutative projective geometry; Sklyanin algebras; Symplectic structures
Subjects: MSC 2010, the AMS's Mathematics Subject Classification > 14 Algebraic geometry
MSC 2010, the AMS's Mathematics Subject Classification > 16 Associative rings and algebras
MSC 2010, the AMS's Mathematics Subject Classification > 18 Category theory; homological algebra
MSC 2010, the AMS's Mathematics Subject Classification > 53 Differential geometry
Depositing User: Ms Lucy van Russelt
Date Deposited: 20 Nov 2007
Last Modified: 20 Oct 2017 14:12
URI: http://eprints.maths.manchester.ac.uk/id/eprint/927

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