  It is a well established fact, that any projective algebraic variety is a
moduli space of representations over some finite dimensional algebra. This
algebra can be chosen in several ways. The counterpart in algebraic geometry is
tautological: every variety is its own Hilber scheme of sheaves of length one.
This holds even scheme theoretic. We use Beilinson's equivalence to get similar
results for finite dimensional algebras, including moduli spaces and quiver
grassmannians. Moreover, we show that several already known results can be
traced back to the Hilbert scheme construction and Beilinson's equivalence.
