Reconstruction of $T_{{\mathbb{P}}^2}$ via tropical Lagrangian multi-section

Abstract

In this paper, we study the reconstruction problem of the holomorphic tangent bundle ${\mathbb{T}}_{{\mathbb{P}}^2}$ of the complex projective plane ${\mathbb{P}}^2$. We introduce the notion of tropical Lagrangian multi-section and cook up one by tropicalizing the Chern connection associated the Fubini-Study metric. Then we perform the reconstruction of ${\mathbb{T}}_{{\mathbb{P}}^2}$ from this tropical Lagrangian multi-section. Walling-crossing phenomenon will occur in the reconstruction process.

14 pages, 2 figures, revised version, to appear in New York Journal of Mathematics

References in corpus (4)

• Lagrangian sections on mirrors of toric Calabi-Yau 3-folds
• Scattering diagrams from asymptotic analysis on Maurer-Cartan equations
• Central charges of T-dual branes for toric varieties
• Bulk-deformed potentials for toric Fano surfaces, wall-crossing and period

Cited by in corpus (1)

• Tropical Lagrangian multi-sections and toric vector bundles