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Regular version of the site

Article

Perverse schobers and birational geometry

Selecta Mathematica, New Series. 2018. Vol. 24. No. 1. P. 85-143.
Alexey Bondal, Kapranov M., Schechtman V.

Perverse schobers are conjectural categorical analogs of perverse sheaves.
We show that such structures appear naturally in Homological Minimal Model Program
which studies the effect of birational transformations such as flops, on the
coherent derived categories. More precisely, the flop data are analogous to hyperbolic
stalks of a perverse sheaf. In the first part of the paper we study schober-type
diagrams of categories corresponding to flops of relative dimension 1, in particular
we determine the categorical analogs of the (compactly supported) cohomology with
coefficients in such schobers. In the second part we consider the example of a “web of
flops” provided by the Grothendieck resolution associated to a reductive Lie algebra g
and study the corresponding schober-type diagram. For g = sl3 we relate this diagram
to the classical space of complete triangles studied by Schubert, Semple and others.