An invariant definition of the operator DELTA of the Batalin-Vilkovisk
y formalism is proposed. It is defined as the divergence of a Hamilton
ian vector field with an odd Poisson bracket (anti-bracket). Its main
properties, which follow from this definition, as well as an example o
f realization of Kahlerian supermanifolds, are considered. The geometr
ical meaning of the Batalin-Vilkovisky formalism is discussed.