Futaki invariants and Yau’s Conjecture on the Hull–Strominger system
Year: 2025
Type: article
Abstract: 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 ) (X,\Omega) 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.
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $2,712
OpenAlex ID: W4408404407