Large quantum corrections in mirror symmetry for a 2-dimensional Lagrangian submanifold with an elliptic umbilic

Giovanni Marelli

Vol. 247 (2010), No. 2, 455–476

DOI: 10.2140/pjm.2010.247.455

Abstract

Given the Lagrangian fibration ℝ⁴ → ℝ² and a Lagrangian submanifold, exhibiting an elliptic umbilic and supporting a flat line bundle, we study in the context of mirror symmetry the corrections necessary to solve the monodromy of the holomorphic structure of the mirror bundle on the dual fibration. This is a preliminary step towards the understanding of quantum corrections in this specific case.

Keywords

mirror symmetry, quantum corrections, elliptic umbilic, Morse homology

Mathematical Subject Classification 2000

Primary: 14J32, 58E05, 58E07

Secondary: 37G25, 53D12

Milestones

Received: 21 December 2008

Revised: 31 May 2010

Accepted: 8 July 2010

Published: 11 August 2010