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...

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Bibliographic Details
Authors: García-Fernández, Mario, González Molina, Raúl
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
Description
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.