On stability conditions for the quintic threefold

Abstract

We study the Clifford type inequality for a particular type of curves $C_{2,2,5}$, which are contained in smooth quintic threefolds. This allows us to prove some stronger Bogomolov-Gieseker type inequalities for Chern characters of stable sheaves and tilt-stable objects on smooth quintic threefolds. Employing the previous framework by Bayer, Bertram, Macrì, Stellari and Toda, we construct an open subset of stability conditions on every smooth quintic threefold in ${\mathbf{P}}_{\mathbb{C}}^4$.

arXiv commentpre-journal version, 32 pages, 7 figures, comments are very welcome!

References in corpus (4)

• Computing the Walls Associated to Bridgeland Stability Conditions on Projective Surfaces
• A generalized Bogomolov-Gieseker inequality for the three-dimensional projective space
• A generalized Bogomolov-Gieseker inequality for the smooth quadric threefold
• Bridgeland Stability Conditions on Fano Threefolds

Cited by in corpus (9)

• Stability conditions in families
• Stability conditions on threefolds with nef tangent bundles
• Rank $r$ DT theory from rank $1$
• On pseudo-Anosov autoequivalences
• Rank $r$ DT theory from rank $0$
• Characteristic classes and stability conditions for projective Kleinian orbisurfaces
• Chern degree functions
• Intrinsic Stabilizer Reduction and Generalized Donaldson-Thomas Invariants
• DHYM connections on higher rank holomorphic vector bundles over $\mathbb{P}(T_{{\mathbb{P}}^2})$