Character varieties of free groups are Gorenstein but not always factorial

Fix a rank g free group F-g and a connected reductive complex algebraic group G. Let chi (F-g, G) be the G-character variety of F-g. When the derived subgroup DG < G is simply connected we show that chi (F-g, G) is factorial (which implies it is Gorenstein), and provide examples to show that when DG is not simply connected chi (F-g, G) need not even be locally factorial. Despite the general failure of factoriality of these moduli spaces, using different methods, we show that chi (F-g, G) is always Gorenstein. (C) 2016 Elsevier Inc. All rights reserved.