Stability conditions on Calabi-Yau double/triple solids
Abstract
In this paper, we prove a stronger form of the Bogomolov-Gieseker (BG) inequality for stable sheaves on two classes of Calabi-Yau threefolds, namely, weighted hypersurfaces inside the weighted projective spaces P(1, 1, 1, 1, 2) and P(1, 1, 1, 1, 4). Using the stronger BG inequality as a main technical tool, we construct open subsets in the spaces of Bridgeland stability conditions on these Calabi-Yau threefolds.
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