| | |
Summary: MIRROR SYMMETRY AND T-DUALITY IN THE COMPLEMENT
OF AN ANTICANONICAL DIVISOR
DENIS AUROUX
Abstract. We study the geometry of complexified moduli spaces of special La-
grangian submanifolds in the complement of an anticanonical divisor in a compact
Kšahler manifold. In particular, we explore the connections between T-duality and
mirror symmetry in concrete examples, and show how quantum corrections arise in
this context.
1. Introduction
The Strominger-Yau-Zaslow conjecture [26] asserts that the mirror of a Calabi-Yau
manifold can be constructed by dualizing a fibration by special Lagrangian tori. This
conjecture has been studied extensively, and the works of Fukaya, Kontsevich and
Soibelman, Gross and Siebert, and many others paint a very rich and subtle picture
of mirror symmetry as a T-duality modified by "quantum corrections" [14, 18, 19].
On the other hand, mirror symmetry has been extended to the non Calabi-Yau set-
ting, and in particular to Fano manifolds, by considering Landau-Ginzburg models,
i.e. noncompact manifolds equipped with a complex-valued function called superpo-
tential [16]. Our goal is to understand the connection between mirror symmetry and
T-duality in this setting.
For a toric Fano manifold, the moment map provides a fibration by Lagrangian
|
