Generalized special Lagrangian fibration for Calabi-Yau hypersurfaces in toric varieties III: The smooth fibres
Wei-Dong Ruan
TL;DR
This paper constructs all smooth torus fibers of generalized special Lagrangian fibrations for Calabi-Yau hypersurfaces in toric varieties near the large complex structure limit, advancing understanding of their geometric structure.
Contribution
It provides a complete construction of smooth fibers in the fibration, a significant step in understanding the SYZ mirror symmetry for Calabi-Yau hypersurfaces.
Findings
Explicit construction of smooth torus fibers
Enhanced understanding of Lagrangian fibrations in toric Calabi-Yau hypersurfaces
Progress towards mirror symmetry conjectures
Abstract
In this paper we construct all smooth torus fibres of the generalized special Lagrangian torus fibrations for Calabi-Yau hypersurfaces in toric varieties near the large complex limit.
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Taxonomy
TopicsGeometry and complex manifolds · Algebraic Geometry and Number Theory · Geometric Analysis and Curvature Flows