  We introduce the notion of a polynomial stability condition, generalizing
Bridgeland stability conditions on triangulated categories. We construct and
study a family of polynomial stability conditions for any normal projective
variety. This family includes both Simpson-stability, and large volume limits
of Bridgeland stability conditions.
  We show that the PT/DT-correspondence relating stable pairs to
Donaldson-Thomas invariants (conjectured by Pandharipande and Thomas) can be
understood as a wall-crossing in our family of polynomial stability conditions.
Similarly, we show that the relation between stable pairs and invariants of
one-dimensional torsion sheaves (proven recently by the same authors) is a
wall-crossing formula.
