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.
- Publication:
-
arXiv e-prints
- Pub Date:
- September 2012
- DOI:
- 10.48550/arXiv.1209.2749
- arXiv:
- arXiv:1209.2749
- Bibcode:
- 2012arXiv1209.2749L
- Keywords:
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- Mathematics - Algebraic Geometry;
- 14D20 (Primary) 14F05;
- 14J10;
- 14J30 (Secondary)
- E-Print:
- 20 pages