Flops and derived categories

D-branes, categories and N=1 supersymmetry

“…In [8] it is proven that D(Coh X) is invariant under a flop transition, a previously known result [6], but the interesting point is the way in which this is proven. This uses the theory of so-called perverse sheaves, which can be formulated using t-structures.…”

“…In [8], one considers perverse sheaves defined by shifting the grading of sheaves supported on an appropriate curve C in the CY by −1. Certain of these perverse sheaves can be identified as analogous to points, and it turns out that the moduli space of these "perverse points" is isomorphic to the CY X ′ which is the result of a flop transition on the curve C.…”

Operations on $ t$-structures and perverse coherent sheaves

“…We expect that important ingredients of the Minimal Model Program, such as flips and flops, could be constructed and understood by means of transformation of t-structures (see [7] for 3-dimensional flops).…”

Stability conditions and Calabi–Yau fibrations

“…In this case, one can construct the heart of perverse t-structure d Per(X/Y ) in the sense of [2]. To introduce this, define C := {c ∈ Coh(X) | Rg * c = 0} and…”