A gluing construction of Z-extremal Kähler metrics and new examples of Bismut Hermitian-Einstein $3$-folds
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(S2× S4)♯ 4(S3× S3), 5(S2× S4)♯ 6(S3× S3) and S1× 9(S2× S3), as well as infinite topological types of smooth compact $7$-dimensional manifolds Y7, providing new solutions to the supersymmetric AdS3 × Y7 type IIB and AdS2 × T2 × Y7 type D=11 supergravity models.
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BibTeX
@misc{apostolov2026gluing,
title = {{A gluing construction of $Z$-extremal Kähler metrics and new examples of Bismut Hermitian-Einstein $3$-folds}},
author = {Vestislav Apostolov and Abdellah Lahdili and Kuan-Hui Lee and Frédéric Rochon},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2609.25250},
eprint = {2609.25250},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.25250},
}
RIS
TY - UNPB
TI - A gluing construction of Z-extremal Kähler metrics and new examples of Bismut Hermitian-Einstein $3$-folds
AU - Vestislav Apostolov
AU - Abdellah Lahdili
AU - Kuan-Hui Lee
AU - Frédéric Rochon
PY - 2026
DA - 2026/10/27
PB - arXiv
DO - 10.48550/arxiv.2609.25250
UR - https://arxiv.org/abs/2609.25250
AB - 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× S^4)♯ 4(S^3× S^3), 5(S^2× S^4)♯ 6(S^3× S^3) and S^1× 9(S^2× S^3), as well as infinite topological types of smooth compact $7$-dimensional manifolds Y_7, providing new solutions to the supersymmetric AdS_3 × Y_7 type IIB and AdS_2 × T^2 × Y^7 type D=11 supergravity models.
ER -