A proof of Lee-Lee's conjecture about geometry of rigid modules

TL;DR

This paper proves Lee-Lee's conjecture, showing a precise correspondence between geometric curves in a punctured disc and algebraic roots of quivers, bridging geometry and representation theory.

Contribution

It establishes a new link between geometric curves and algebraic roots, confirming Lee-Lee's conjecture in the context of quiver representations.

Findings

Confirmed the coincidence between associated roots of non-self-intersecting curves and real Schur roots.

Established a geometric interpretation of algebraic roots in the setting of punctured discs.

Bridged the gap between geometric topology and algebraic representation theory.

Abstract

This paper proves Lee-Lee's conjecture that establishes a coincidence between the set of associated roots of non-self-intersecting curves in a $n$-punctured disc and the set of real Schur roots of acyclic (valued) quivers with $n$ vertices.