July 20, 2026, 10:00 +0200
Padova, Torre Archimede 7B1

A geometric model for the perfect derived category of pinched gentle algebras

Pierre Bodin, Université Grenoble Alpes

Abstract

By the work of Opper, Plamondon and Schroll, indecomposable objects in the bounded derived category of a graded gentle algebra are in bijection with homotopy classes of graded curves on the corresponding graded marked surface. We first recall the bijection between pinched gentle algebras, an enlargement of the class of gentle algebras, and graded marked surfaces with conical singularities endowed with an admissible dissection. We then use the result of Opper, Plamondon and Schroll to classify the indecomposable objects in their perfect derived categories in terms of homotopy classes of graded curves on the singular surface. We also give a geometric interpretation for the possible decompositions of a given object into different direct sums of indecomposable objects.