Compactifications of spaces of Landau-Ginzburg models

TL;DR

This paper reviews techniques for compactifying Landau-Ginzburg models, explores their relation to stability and quiver representations, and surveys applications to the birational geometry of del Pezzo surfaces.

Contribution

It applies previous methods to basic examples, establishing links between Landau-Ginzburg models, stability conditions, and birational geometry.

Findings

Relationship between $A_n$ categories and stability conditions

Connections to directed quiver representations

Applications to birational geometry of del Pezzo surfaces

Abstract

This paper reviews results and techniques from the authors' previous work "Symplectomorphism group relations and degenerations of Landau-Ginzburg models" and applies them in basic examples. The main example is the $A_n$ category where we observe a relationship to stability conditions and directed quiver representations. We conclude with a brief survey of applications to the birational geometry of del Pezzo surfaces.