A gluing construction of $Z$-extremal Kähler metrics and new examples of Bismut Hermitian-Einstein $3$-folds
Year: 2026
Type: preprint
Abstract: We present a gluing construction for a class of 6th order geometric non-linear PDE's on a Kähler manifold or orbifold, arising in the study of Bismut Hermitian Einstein complex $3$-folds, the supersymmetric supergravity models in physics, and in Dervan's Z-critical Kähler metrics. As applications, we obtain a desingularization theorem for orbifolds with crepant singularities admitting a solution of the PDE, as well as a blowing-up of points theorem for smooth complex $3$-folds admitting such solutions. These results yield new examples of regular Bismut Hermitian Einstein structures on the smooth manifolds $3(S^2\times S^4)\sharp 4(S^3\times S^3)$, $5(S^2\times S^4)\sharp 6(S^3\times S^3)$ and $S^1\times 9(S^2\times S^3)$, as well as infinite topological types of smooth compact $7$-dimensional manifolds $Y_7$, providing new solutions to the supersymmetric ${\rm AdS}_3 \times Y_7$ type IIB and ${\rm AdS}_2 \times T^2 \times Y^7$ type $D=11$ supergravity models.
Source: arXiv (Cornell University)
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Award: G4998900716
OpenAlex ID: W7214113942