New Solutions to the $G_2$ Hull-Strominger System via torus fibrations over $K3$ orbifolds
Anna Fino, Gueo Grantcharov, Jose Medel
TL;DR
This paper constructs new smooth solutions to the $G_2$ Hull-Strominger system using torus fibrations over singular K3 surfaces, expanding the known landscape of solutions in differential geometry.
Contribution
It introduces a novel method of constructing solutions via torus fibrations over singular K3 orbifolds, utilizing primitive divisors and adapted Serre construction.
Findings
New smooth solutions to the $G_2$ Hull-Strominger system
Use of torus fibrations over singular K3 surfaces
Application of adapted Serre construction in singular setting
Abstract
Using torus fibrations over K3 orbisurfaces, we construct new smooth solutions to the Hull-Strominger system. These manifolds arise as total spaces of principal (orbi)bundles over singular K3 surfaces. Our construction is based on the choice of three divisors on a singular K3 surface that are primitive with respect to a particular K\"ahlermetric. The stable bundle is obtained via an adaptation of the Serre construction to the singular setting.
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Taxonomy
TopicsGeometry and complex manifolds · Algebraic Geometry and Number Theory · Geometric Analysis and Curvature Flows