Polynomial Bridgeland stability conditions for thederived category of sheaves on surfaces

摘要

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 [2] (see also [19. 20]). 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 [16, 17]. Furthermore, when the polarization is contained in a chamber, we show that the polynomial Bridgeland stability and Gieseker stability can be identified.