Tropical Lagrangian multi-section and smoothing of locally sheaves over degenerated Calabi-Yau surfaces

Abstract: Homological mirror symmetry suggests that Lagrangian multi-sections over an integral affine manifold with singularities $B$ should mirror to holomorphic vector bundles. In this talk, I will introduce the tropical version of Lagrangian multi-sections, called tropical Lagrangian multi-sections. I will mainly focus on dimension 2. To certain tropical Lagrangian multi-sections over $B$, I will construct a locally free sheaf $E_0$ on the log Calabi-Yau surface $X_0(B)$ associated to $B$ and study the smoothability of the pair $(X_0(B),E_0)$. This is a joint work with Kwokwai Chan and Ziming Ma.

Mathematics

Audience: researchers in the topic

ICCM 2020