Perverse coherent t-structures through torsion theories

Bezrukavnikov (later together with Arinkin) recovered the work of Deligne defining perverse $t$-structures for the derived category of coherent sheaves on a projective variety. In this text we prove that these $t$-structures can be obtained through tilting torsion theories as in the work of Happel, Reiten and Smal\o. This approach proves to be slightly more general as it allows us to define, in the quasi-coherent setting, similar perverse $t$-structures for certain noncommutative projective planes.Comment: New revised version with important correction

Generalized N=(2,2) Supersymmetric Non-Linear Sigma Models

We rewrite the N=(2,2) non-linear sigma model using auxiliary spinorial superfields defining the model on ${\cal T}\oplus^ *{\cal T}$, where ${\cal T}$ is the tangent bundle of the target space. This is motivated by possible connections to Hitchin's generalized complex structures. We find the general form of the second supersymmetry compatible with that of the original model.Comment: 13 pages, Latex Minor corrections to agree with published versio