Rigid HYM Connections on Tautological Bundles over ALE Crepant Resolutions in Dimension Three
Name
Degeratu-2016-Rigid HYM Connection.pdf
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526.79 KB
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Author(s)
Degeratu, Anda
Walpuski, Thomas
Date Issued
February 2016
Journal
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
Abstract
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.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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Creative Commons Attribution
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DOI of Published Version
https://doi.org/10.3842/sigma.2016.017
