Mathematical Research Letters

Volume 19 (2012)

Number 4

Polynomial bridgeland stable objects and reflexive sheaves

Pages: 873 – 885

DOI: http://dx.doi.org/10.4310/MRL.2012.v19.n4.a11

Author

Jason Lo (Department of Mathematics, University of Missouri-Columbia, Columbia, Mo., U.S.A.)

Abstract

On a smooth projective threefold X, we show that there are only two isomorphism types for the moduli of stable objects with respect to Bayer’s standard polynomial Bridgeland stability — the moduli of Gieseker-stable sheaves and the moduli of PT-stable objects — under the following assumptions: no two of the stability vectors are collinear, and the degree and rank of the objects are relatively prime. We also interpret the intersection of the moduli spaces of PT-stable and dual-PT-stable objects as a moduli of reflexive sheaves, and point out its connections with the existence problem of Bridgeland stability conditions on smooth projective threefolds, and the existence of fine moduli spaces of complexes on elliptic threefolds.

Keywords

derived category, moduli, polynomial stability, reflexive sheaves

2010 Mathematics Subject Classification

Primary 14F05, 14J10, 14J60. Secondary 14J30.

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