Futaki invariants and Yau's Conjecture on the Hull-Strominger system
We find a new obstruction to the existence of solutions of the Hull-Strominger system, which goes beyond the balanced property of the Calabi-Yau manifold (X, ω) and the Mumford-Takemoto slope stability of the bundle over it. The basic principle is the construction of a (possibly indefinite) Hermitia...
| Authors: | , |
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| Format: | article |
| Status: | Published version |
| Publication Date: | 2025 |
| Country: | España |
| Institution: | Consejo Superior de Investigaciones Científicas (CSIC) |
| Repository: | DIGITAL.CSIC. Repositorio Institucional del CSIC |
| OAI Identifier: | oai:digital.csic.es:10261/422702 |
| Online Access: | http://hdl.handle.net/10261/422702 https://api.elsevier.com/content/abstract/scopus_id/105000203936 |
| Access Level: | Open access |
| Summary: | We find a new obstruction to the existence of solutions of the Hull-Strominger system, which goes beyond the balanced property of the Calabi-Yau manifold (X, ω) and the Mumford-Takemoto slope stability of the bundle over it. The basic principle is the construction of a (possibly indefinite) Hermitian Einstein metric on the holomorphic string algebroid associated to a solution of the system, provided that the connection on the tangent bundle is Hermitian Yang-Mills. Using this, we define a family of Futaki invariants obstructing the existence of solutions in a given balanced class. Our results are motivated by a strong version of a conjecture by Yau on the existence problem for these equations. |
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