2008/06/16 by Paul S. Aspinwall, Aspinwall, Paul S. · 4 citations
Mathematics · Physics and Astronomy · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #Black Holes and Theoretical Physics #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #hep-th #math.AG
paper · pdf · doi:10.48550/arxiv.0806.2612
28 pages, counterexample to global tilting set added, refs added, conventions made more sane
openalex publication_date 2008/06/16 · arxiv created 2009/05/13 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We analyze B-type D-branes on noncompact toric Calabi--Yau spaces. A general program is presented to find a set of tilting line bundles that yields the associated quiver and its relations. In many cases, this set remains fixed as one moves between phases in the Kähler moduli space. This gives a particularly simple picture of how the derived category remains invariant across all phases. The combinatorial problems involving local cohomology used to determine the tilting set are also related to questions of Pi-stability as one moves between phases. As a result, in some cases precisely those line bundles in the tilting set remain stable over the whole moduli space in some sense.