Tropical Lagrangian multi-sections and tropical locally free sheaves

Abstract

This article is a continuation of the work "Tropical Lagrangian multi-sections and smoothing of locally free sheaves over degenerated Calabi-Yau surfaces". We generalize the notion of tropical Lagrangian multi-sections to any dimensions. Together with some linear algebra data, we construct a special class of locally free sheaves, called tropical locally free sheaves. We will also provide the reverse construction and show that there is a 1-1 correspondence between isomorphism classes of tropical locally free sheaves and tropical Lagrangian multi-sections modulo certain equivalence.