[HG_AG] Tropical Lagrangian multi-sections and locally free sheaves
ABSTRACT
The Gross-Siebert program is usually referred to as the algebraic version of the famous SYZ mirror symmetry. The fundamental tool in their program is tropical geometry. A natural question that we want to address is how can one understand homological mirror symmetry under the Gross-Siebert framework. In this talk, I am going to introduce the notion of tropical Lagrangian multi-sections, which is a combinatorial replacement of Lagrangian multi-sections in the SYZ proposal. Such tropical objects can be used to construct locally free sheaves on log Calabi-Yau varieties. I will discuss the construction and smoothability of these locally free sheaves that arise from tropical geometry.