  We generalize Lusztig's nilpotent varieties, and Kashiwara and Saito's
geometric construction of crystal graphs from the symmetric to the
symmetrizable case. We also construct semicanonical functions in the
convolution algebras of generalized preprojective algebras. Conjecturally these
functions yield semicanonical bases of the enveloping algebras of the positive
part of symmetrizable Kac-Moody algebras.
