Perverse schobers and birational geometry

摘要: 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 birational transformations as flops, on coherent derived categories. More precisely, flop data analogous to hyperbolic stalks a sheaf. In first part paper we study schober-type diagrams categories corresponding flops relative dimension 1, particular determine (compactly supported) cohomology with coefficients schobers. second consider example “web flops” provided by Grothendieck resolution associated reductive Lie algebra \(\mathfrak {g}\) and diagram. For {g}={\mathfrak {s}\mathfrak {l}}_3\) relate this diagram classical space complete triangles studied Schubert, Semple others.