Real variations of stability conditions for noncommutative symplectic resolutions

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A localization theorem for the cyclotomic rational Cherednik algebra Hc=Hc((Z/l)ⁿ Sₙ) over a field of positive characteristic has been proved by Bezrukavnikov, Finkelberg and Ginzburg. Localizations with different parameters give different t-structures on the derived category of coherent sheaves on the Hilbert scheme of points on a surface. In this short note, we concentrate on the comparison between different t-structures coming from different localizations. When n=2, we show an explicit construction of tilting bundles that generates these t-structures. These t-structures are controlled by a real variation of stability conditions, a notion related to Bridgeland stability conditions. We also show its relation to the topology of Hilbert schemes and irreducible representations of Hc.