Some examples of tilt-stable objects on threefolds

Abstract

We investigate properties and describe examples of tilt-stable objects on a smooth complex projective threefold. We give a structure theorem on slope semistable sheaves of vanishing discriminant, and describe certain Chern classes for which every slope semistable sheaf yields a Bridgeland semistable object of maximal phase. Then, we study tilt stability as the polarisation $\omega$ gets large, and give sufficient conditions for tilt-stability of sheaves of the following two forms: 1) twists of ideal sheaves or 2) torsion-free sheaves whose first Chern class is twice a minimum possible value.

20 pages

References in corpus (6)

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• Moduli of PT-Semistable Objects I
• Bridgeland Stability conditions on threefolds I: Bogomolov-Gieseker type inequalities
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Cited by in corpus (4)

• The Space of Stability Conditions on Abelian Threefolds, and on some Calabi-Yau Threefolds
• Fourier-Mukai Transforms and Bridgeland Stability Conditions on Abelian Threefolds II
• Torsion pairs and filtrations in abelian categories with tilting objects
• Preservation of semistability under Fourier-Mukai transforms