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.

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

References in corpus (1)

• Stability conditions, Bogomolov-Gieseker type inequalities and Fano 3-folds

Cited by in corpus (5)

• Curve counting and S-duality
• Rank $r$ DT theory from rank $0$
• On the Bogomolov-Gieseker inequality in positive characteristic
• On the Bogomolov-Gieseker inequality for hypersurfaces in the projective spaces
• Stability condition on Calabi-Yau threefold of complete intersection of quadratic and quartic hypersurfaces