Stability Conditions on Threefolds - Some Wall-Crossings
The theory of Bridgeland stability conditions has lead to deep results about the geometry of moduli spaces of sheaves on surfaces. One of the main obstacles to do the same on threefolds is the construction of stability conditions. Recent progress on this question in special cases raises the question whether the corresponding moduli spaces can be studied. I will present an approach that uses computations similar to those on surfaces. In the case of projective space, I will show examples of concrete wall-crossing behavior for some Hilbert schemes of curves.