2012/07/31 by Anda Degeratu, Thomas Walpuski
Mathematics · Physics and Astronomy · #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebra over a field #Calabi–Yau manifold #Dimension (graph theory) #Geometry #Mathematics #Nonlinear Waves and Solitons #Pure mathematics #math.AG #math.DG
paper · pdf · doi:10.3842/sigma.2016.017
published as SIGMA 12 (2016), 017, 23 pages
arxiv created 2016/02/15 · openalex publication_date 2016/02/15 · arxiv updated 2016/02/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
For G a finite subgroup of SL(3, C) acting freely on C 3 \0 a crepant resolution of the Calabi-Yau orbifold C 3 /G always exists and has the geometry of an ALE non-compact manifold. We show that the tautological bundles on these crepant resolutions admit rigid Hermitian-Yang-Mills connections. For this we use analytical information extracted from the derived category McKay correspondence of Bridgeland, King, and Reid [J. Amer. Math. Soc. 14 (2001), 535-554]. As a consequence we rederive multiplicative cohomological identities on the crepant resolution using the Atiyah-Patodi-Singer index theorem. These results are dimension three analogues of Kronheimer and Nakajima's results [Math. Ann. 288 (1990), 263-307] in dimension two.