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Rigid HYM Connections on Tautological Bundles over ALE Crepant Resolutions in Dimension Three
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...
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Інститут математики НАН України
2016
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| Series: | Symmetry, Integrability and Geometry: Methods and Applications |
| Online Access: | http://dspace.nbuv.gov.ua/handle/123456789/147430 |
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irk-123456789-1474302019-02-15T01:24:25Z Rigid HYM Connections on Tautological Bundles over ALE Crepant Resolutions in Dimension Three Degeratu, A. Walpuski, T. 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. 2016 Article 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 en Symmetry, Integrability and Geometry: Methods and Applications Інститут математики НАН України |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine |
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English |
| 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. |
| format |
Article |
| author |
Degeratu, A. Walpuski, T. |
| spellingShingle |
Degeratu, A. Walpuski, T. Rigid HYM Connections on Tautological Bundles over ALE Crepant Resolutions in Dimension Three Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Degeratu, A. Walpuski, T. |
| author_sort |
Degeratu, A. |
| title |
Rigid HYM Connections on Tautological Bundles over ALE Crepant Resolutions in Dimension Three |
| title_short |
Rigid HYM Connections on Tautological Bundles over ALE Crepant Resolutions in Dimension Three |
| title_full |
Rigid HYM Connections on Tautological Bundles over ALE Crepant Resolutions in Dimension Three |
| title_fullStr |
Rigid HYM Connections on Tautological Bundles over ALE Crepant Resolutions in Dimension Three |
| title_full_unstemmed |
Rigid HYM Connections on Tautological Bundles over ALE Crepant Resolutions in Dimension Three |
| title_sort |
rigid hym connections on tautological bundles over ale crepant resolutions in dimension three |
| publisher |
Інститут математики НАН України |
| publishDate |
2016 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/147430 |
| citation_txt |
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. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
| work_keys_str_mv |
AT degeratua rigidhymconnectionsontautologicalbundlesoveralecrepantresolutionsindimensionthree AT walpuskit rigidhymconnectionsontautologicalbundlesoveralecrepantresolutionsindimensionthree |
| first_indexed |
2023-05-20T17:27:40Z |
| last_indexed |
2023-05-20T17:27:40Z |
| _version_ |
1796153342105223168 |