Birational Calabi-Yau 3-folds and BPS state counting

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

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Algebraic Geometry, 14E30, 14D20, 18E30,

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http://salesiana.dossiersoluciones.com/handle/123456789/156845

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/0707.1643
 http://arxiv.org/abs/0707.1643

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arXiv