Invariant theory of canonical algebras

Based on the first fundamental theorem of classical invariant theory we pre sent a reduction technique for computing relative invariants for quivers wi th relations. This is applied to the invariant theory of canonical algebras and yields an explicit construction of the moduli spaces (together with th e quotient morphisms from the corresponding representation spaces) for fami lies of modules with a fixed dimension vector belonging to the central sinc ere separating subcategory. By means of a tilting process we extend these r esults to the invariant theory of concealed-canonical algebras, thus coveri ng the cases of tame hereditary, tame concealed, and tubular algebras, resp ectively. Our approach yields, in particular, a uniform treatment to an ess ential part of the invariant theory of extended Dynkin quivers, a topic pop ular over the years, but stretches far beyond since also concealed-canonica l algebras of tubular or wild representation type are covered. (C) 2000 Aca demic Press.