  The derived categories of toric varieties admit semi-orthogonal
decompositions coming from wall-crossing in GIT. We prove that these
decompositions satisfy a Jordan-Holder property: the subcategories that appear,
and their multiplicities, are independent of the choices made.
  For Calabi-Yau toric varieties wall-crossing instead gives derived
equivalences and autoequivalences, and mirror symmetry relates these to
monodromy around the GKZ discriminant locus. We formulate a conjecture equating
intersection multiplicities in the discriminant with the multiplicities
appearing in certain semi-orthogonal decompositions. We then prove this
conjecture in some cases.
