Self-Duality for Landau--Ginzburg models

TL;DR

This paper explores mirror symmetry as a duality between Landau-Ginzburg models, identifying specific cases where self-duality occurs, notably in cotangent bundles and the resolved conifold, with examples on vector bundles over the projective line.

Contribution

It provides explicit examples of self-duality in Landau-Ginzburg models, expanding understanding of mirror symmetry in specific geometric contexts.

Findings

Self-duality occurs in cotangent bundle and resolved conifold cases.

Examples involve vector bundles over the projective line.

Clarifies conditions for self-duality in LG models.

Abstract

P. Clarke describes mirror symmetry as a duality between Landau--Ginzburg models, so that the dual of an LG model is another LG model. We describe examples in which the underlying space is a total space of a vector bundle on the projective line, and we show that self-duality occurs in precisely two cases: the cotangent bundle and the resolved conifold.