The AG-invariant for (m+2)-angulations

TL;DR

This paper introduces a method to compute the AG-invariant for gentle algebras derived from (m+2)-angulations of unpunctured Riemann surfaces, generalizing previous work for m=1.

Contribution

It provides a new calculation method for the AG-invariant based on the configuration of arcs, marked points, and boundary components in (m+2)-angulations.

Findings

Derived invariant calculation method for (m+2)-angulations

Generalization of previous m=1 case

Application to gentle algebras from Riemann surfaces

Abstract

In this paper, we study gentle algebras that come from (m+2)-angulations of unpunctured Riemann surfaces with boundary and marked points. We focus on calculating a derived invariant introduced by Avella-Alaminos and Geiss, generalizing previous work done when m=1. In particular, we provide a method for calculating this invariant based on the the configuration of the arcs in the (m+2)-angulation, the marked points, and the boundary components.