Birational Calabi-Yau 3-folds and BPS state counting
Algebraic Geometry
2008-03-16 v3
Abstract
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.
Keywords
Cite
@article{arxiv.0707.1643,
title = {Birational Calabi-Yau 3-folds and BPS state counting},
author = {Yukinobu Toda},
journal= {arXiv preprint arXiv:0707.1643},
year = {2008}
}
Comments
Some explanations and proofs are added. To appear in Communications in Number Theory and Physics