Abstract
We consider the problem of comparing t-structures under the derived McKay correspondence and for tilting equivalences. In low-dimensional cases, we relate the t-structures via torsion theories arising from additive functions on the triangulated category. As an application, we give a criterion for rationality for surfaces with a tilting bundle. We also show that every smooth projective surface that admits a full, strong, and exceptional collection of line bundles is rational.
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