  We discuss the geometry of the Lagrangian quantization scheme based on
(generalized) Schwinger-Dyson BRST symmetries. When a certain set of ghost
fields are integrated out of the path integral, we recover the
Batalin-Vilkovisky formalism, now extended to arbitrary functional measures for
the classical fields. Keeping the ghosts reveals the crucial role played by a
natural connection on the space of fields.
