Birational Calabi-Yau 3-folds and BPS state counting

2007/07/11 by Yukinobu Toda, Toda, Yukinobu · 1 citation
Mathematics · #14D20 #14E30 #18E30 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.0707.1643

openalex publication_date 2007/07/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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• Derived categories of small toric Calabi-Yau 3-folds and counting invariants

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