The closure of the set of periodic modules over a concealed canonical algebra is regular in codimension one

TL;DR

This paper proves that for a concealed canonical algebra, the union of orbit closures of periodic modules with a fixed dimension vector forms a set that is both closed and exhibits regularity in codimension one.

Contribution

It establishes the regularity in codimension one of the union of orbit closures of periodic modules over a concealed canonical algebra, a new geometric property.

Findings

The union of orbit closures is closed.

The set is regular in codimension one.

Applicable to modules with fixed dimension vector d.

Abstract

Let A be a concealed canonical algebra and d the dimension vector of an A-module which is periodic respect to the action of the Auslander-Reiten translation In the paper, we investigate the union of the closures of the orbits of the periodic A-modules of dimension vector d. We show that this set is closed and regular in codimension one.