Homological Mirror Symmetry for Local Calabi-Yau Manifolds via SYZ

Abstract

This is a write-up of the author's talk in the conference Algebraic Geometry in East Asia 2016 held at the University of Tokyo in January 2016. We give a survey on the series of papers [16,24, 23,22] where the author and his collaborators Daniel Pomerleano and Kazushi Ueda show how Strominger-Yau-Zaslow (SYZ) transforms can be applied to understand the geometry of Kontsevich's homological mirror symmetry (HMS) conjecture for certain local Calabi-Yau manifolds.

The SYZ Conjecture via Homological Mirror Symmetry

“…Torsion sheaves are successive extensions of skyscrapers at points which correspond to S 1 fibers of µ : X → B. For more recent work on understanding the SYZ transform see [Cha16] and the references therein.…”