Character Varieties of Free Groups are Gorenstein but not always Factorial
arXiv:1504.01210 · doi:10.1016/j.jalgebra.2016.01.044
Abstract
Fix a rank g free group F and a connected reductive complex algebraic group G. Let X(F,G) be the G-character variety of F. When the derived subgroup DG in G is simply connected we show that X(F,G) is factorial (which implies it is Gorenstein), and provide examples to show that when DG is not simply connected X(F,G) need not even be locally factorial. Despite the general failure of factoriality of these moduli spaces, using different methods, we show that X(F,G) is always Gorenstein.
11 pages, 3 figures; accepted for publication in the Journal of Algebra