  In the case of toric varieties, we continue the pursuit of Kontsevich's
fundamental insight, Homological Mirror Symmetry, by unifying it with the Mori
program. We give a refined conjectural version of Homological Mirror Symmetry
relating semi-orthogonal decompositions of the $B$-model on toric varieties to
semi-orthogonal decompositions on the $A$-model on the mirror Landau-Ginzburg
models.
  As evidence, we prove a new case of Homological Mirror Symmetry for a toric
surface whose anticanonical bundle is not nef, namely a certain blow-up of
$\P^2$ at three infinitesimally near points.
