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 $\mathbb{P}(1,1,1,1,2)$ and $\mathbb{P}(1,1,1,1,4)$. 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.

arXiv comment34 pages, 4 figures, improvements based on the referee's comments, to appear in Forum of Mathematics, Sigma

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