Generating sets for coordinate rings of character varieties
  We find finite, reasonably small, generator sets of the coordinate rings of G-character varieties of finitely generated groups for all classical groups G. This result together with the method of Grobner basis gives an algorithm for describing character varieties by explicit polynomial equations.   Additionally, we describe finite sets of generators of the fields of rational functions on G-character varieties for all exceptional algebraic groups G. 
Adam S. Sikora
math.AG math.RT