%0 Journal Article
%T Curve counting theories via stable objects II: DT/ncDT flop formula
%A Yukinobu Toda
%J Mathematics
%D 2009
%I arXiv
%X The goal of the present paper is to show the transformation formula of Donaldson-Thomas invariants on smooth projective Calabi-Yau 3-folds under birational transformations via categorical method. We also generalize the non-commutative Donaldson-Thomas invariants, introduced by B. Szendr{\H o}i in a local $(-1, -1)$-curve example, to an arbitrary flopping contraction from a smooth projective Calabi-Yau 3-fold. The transformation formula between such invariants and the usual Donaldson-Thomas invariants are also established. These formulas will be deduced from the wall-crossing formula in the space of weak stability conditions on the derived category.
%U http://arxiv.org/abs/0909.5129v3