Rigid HYM Connections on Tautological Bundles over ALE Crepant Resolutions in Dimension Three
Vernadsky National Library of Ukraine
Переглянути архів Інформація| Поле | Співвідношення | |
| Title |
Rigid HYM Connections on Tautological Bundles over ALE Crepant Resolutions in Dimension Three
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| Creator |
Degeratu, A.
Walpuski, T. |
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| Description |
For G a finite subgroup of SL(3,C) acting freely on C³∖{0} a crepant resolution of the Calabi-Yau orbifold C³/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.
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| Date |
2019-02-14T18:31:47Z
2019-02-14T18:31:47Z 2016 |
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| Type |
Article
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| Identifier |
Rigid HYM Connections on Tautological Bundles over ALE Crepant Resolutions in Dimension Three / A. Degeratu, T. Walpuski // Symmetry, Integrability and Geometry: Methods and Applications. — 2016. — Т. 12. — Бібліогр.: 29 назв. — англ.
1815-0659 2010 Mathematics Subject Classification: 53C07; 14F05; 58J20 DOI:10.3842/SIGMA.2016.017 http://dspace.nbuv.gov.ua/handle/123456789/147430 |
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| Language |
en
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| Relation |
Symmetry, Integrability and Geometry: Methods and Applications
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| Publisher |
Інститут математики НАН України
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