Rigid HYM Connections on Tautological Bundles over ALE Crepant Resolutions in Dimension Three
Author(s)
Degeratu, Anda; Walpuski, Thomas
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For G a finite subgroup of SL(3,C) acting freely on C[superscript 3]\{0} a crepant resolution of the Calabi-Yau orbifold C[superscript 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.
Date issued
2016-02Department
Massachusetts Institute of Technology. Department of MathematicsJournal
Symmetry, Integrability and Geometry: Methods and Applications
Publisher
National Academy of Sciences of Ukraine (SIGMA (Symmetry, Integrability, and Geometry: Methods and Application))
Citation
Degeratu, Anda, and Thomas Walpuski. “Rigid HYM Connections on Tautological Bundles over ALE Crepant Resolutions in Dimension Three.” SIGMA (February 15, 2016).
Version: Final published version
ISSN
1815-0659