Reconstruction of holomorphic tangent bundle of complex projective plane via tropical Lagrangian multi-section. (Reconstruction of holomoprhic tangent bundle of complex projective plane via tropical Lagrangian multi-section.) (English) Zbl 1467.53090
Summary: In this paper, we study the reconstruction problem of the holomorphic tangent bundle of the complex projective plane. We introduce the notion of tropical Lagrangian multi-section and cook up one tropicalizing the Chern connection associated the Fubini-Study metric. Then we perform the reconstruction of the tangent bundle from this tropical Lagrangian multi-section. Walling-crossing phenomenon will occur in the reconstruction process.
MSC:
| 53D37 | Symplectic aspects of mirror symmetry, homological mirror symmetry, and Fukaya category |
| 14J33 | Mirror symmetry (algebro-geometric aspects) |
| 53-11 | Research data for problems pertaining to differential geometry |
| 14J32 | Calabi-Yau manifolds (algebro-geometric aspects) |
| 53D40 | Symplectic aspects of Floer homology and cohomology |
| 14T20 | Geometric aspects of tropical varieties |
| 32Q25 | Calabi-Yau theory (complex-analytic aspects) |
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