Communications in Analysis and Geometry

Volume 19 (2011)

Number 1

Polynomial Bridgeland stability conditions for the derived category of sheaves on surfaces

Pages: 31 – 52



Wei-Ping Li (Department of Mathematics, Hong Kong University of Science & Technology)

Zhenbo Qin (Department of Mathematics, University of Missouri at Columbia)


For the derived category of bounded complexes of coherent sheaves on a smooth projective surface, we study the standard polynomial Bridgeland stability conditions introduced by Bayer. Assuming certain conditions on the stability vector, we prove that the standard polynomial Bridgeland stability remains to be the same when the polarization varies in a chamber in the usual sense of Qin and Sze. Furthermore, when the polarization is contained in a chamber, we show that the polynomial Bridgeland stability and Gieseker stability can be identified.

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