I will explain how to view the construction of moduli spaces of
semistable sheaves on a projective variety as a functorial embedding into
more basic projective varieties, namely moduli spaces of semistable
Kronecker modules. This sheds new light on how to construct 'theta
functions', i.e. natural projective coordinates on these moduli spaces.
This is joint work with Alastair King (Invent. Math. 168 (2007) 613-666).