The geometry of variations in Batalin–Vilkovisky formalism

We explain why no sources of divergence are built into the Batalin–Vilkovisky (BV) Laplacian, whence there is no need to postulate any ad hoc conventions such as "δ(0) 0" and "log δ(0) 0" within BV-approach to quantisation of gauge systems. Remarkably, the geometry of iterated variations does not refer at all to the construction of Dirac's δ-function as a limit of smooth kernels. We illustrate the reasoning by re-deriving –but not just 'formally postulating' – the standard properties of BV-Laplacian and Schouten bracket and by verifying their basic inter-relations (e.g., cohomology preservation by gauge symmetries of the quantum master-equation).