## 2007.183: Sklyanin algebras and Hilbert schemes of points

2007.183:
T.A. Nevins and J.T. Stafford
(2006)
*Sklyanin algebras and Hilbert schemes of points.*
Advances in Mathematics, 210 (2).
pp. 405-478.
ISSN 0001-8708

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DOI: 10.1016/j.aim.2006.06.009

## 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 |
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Uncontrolled Keywords: | Moduli spaces; Hilbert schemes; Noncommutative projective geometry; Sklyanin algebras; Symplectic structures |

Subjects: | MSC 2000 > 14 Algebraic geometry MSC 2000 > 16 Associative rings and algebras MSC 2000 > 18 Category theory; homological algebra MSC 2000 > 53 Differential geometry |

MIMS number: | 2007.183 |

Deposited By: | Mrs Louise Healey |

Deposited On: | 20 November 2007 |

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