Abelian fibrations and SYZ mirror conjecture

TL;DR

This paper explores the SYZ mirror conjecture by constructing dual fibrations of polarized abelian varieties and demonstrating their equivalence at the derived category level, advancing understanding of mirror symmetry.

Contribution

It constructs dual fibrations of polarized abelian varieties and proves their derived category equivalence, providing new insights into the SYZ mirror conjecture.

Findings

Constructed dual fibrations of polarized abelian varieties.

Proved derived category equivalence of the dual fibrations.

Supported the SYZ mirror conjecture with new mathematical evidence.

Abstract

SYZ mirror conjecture predicts that a Calabi-Yau manifold $X$ consists of a family of tori which are dual to a family of special lagrangian tori on the mirror dual manifold $\hat{X}$. Here we consider a fibration of polarized abelian varieties and we construct a dual one. Moreover we prove that they are equivalent at the level of derived categories.