Birational Calabi-Yau 3-folds and BPS state counting

Details Birational Calabi-Yau 3-folds and BPS state counting Birational Calabi-Yau 3-folds and BPS state counting

2007-07-11

arxiv.org/abs/0707.1643v3

Mathematics

Algebraic Geometry

Some explanations and proofs are added. To appear in Communications in Number Theory and Physics

Scientific paper

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.

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