%0 Journal Article
%T Birational Calabi-Yau 3-folds and BPS state counting
%A Yukinobu Toda
%J Mathematics
%D 2007
%I arXiv
%X This paper contains some applications of Bridgeland-Douglas stability conditions on triangulated categories, and Joyce's work on counting invariants of semistable objects, to the study of birational geometry. We introduce the notion of motivic Gopakumar-Vafa invariants as counting invariants of D2-branes, and show that they are invariant under birational transformations between Calabi-Yau 3-folds. The result is similar to the fact that birational Calabi-Yau 3-folds have the same betti numbers or Hodge numbers.
%U http://arxiv.org/abs/0707.1643v3