English

Matrix factorizations from SYZ transformations

Symplectic Geometry 2013-01-30 v1 Algebraic Geometry

Abstract

It is known that Lagrangian torus fibers of the moment map of a toric Fano manifold XX, equipped with flat U(1)U(1)-connections, are mirror to matrix factorizations of the mirror superpotential W:Xˇ\bCW:\check{X}\rightarrow\bC. Via SYZ mirror transformations, we describe how this correspondence, when XX is \bP1\bP^1 or \bP2\bP^2, can be explained in a geometric way.

Keywords

Cite

@article{arxiv.1006.3832,
  title  = {Matrix factorizations from SYZ transformations},
  author = {Kwokwai Chan and Naichung Conan Leung},
  journal= {arXiv preprint arXiv:1006.3832},
  year   = {2013}
}

Comments

20 pages. Dedicated to Prof. S.-T. Yau on the occasion of his 60th birthday

R2 v1 2026-06-21T15:38:27.461Z