Counting using Hall Algebras II. Extensions from Quivers

Abstract

We count the Fq-rational points of GIT quotients of quiver representations with relations. We focus on two types of algebras -one is one-point extended from a quiver Q, and the other is the Dynkin A 2 tensored with Q. For both, we obtain explicit formulas. We study when they are polynomial-count. We follow the similar line as in the first paper but algebraic manipulations in Ringel-Hall algebra will be replaced by corresponding geometric constructions.