  We formulate the abelian six-dimensional $\mathcal{N}=(2,0)$ theory
perturbatively, in a generalization of the Batalin-Vilkovisky formalism. Using
this description, we compute the holomorphic and non-minimal twists at the
perturbative level. This calculation hinges on the existence of an $L_\infty$
action of the supersymmetry algebra on the abelian tensor multiplet, which we
describe in detail. Our formulation appears naturally in the pure spinor
superfield formalism, but understanding it requires developing a presymplectic
generalization of the BV formalism, inspired by Dirac's theory of constraints.
The holomorphic twist consists of symplectic-valued holomorphic bosons from the
$\mathcal{N}=(1,0)$ hypermultiplet, together with a degenerate holomorphic
theory of holomorphic coclosed one-forms from the $\mathcal{N}=(1,0)$ tensor
multiplet, which can be interpreted as representing the intermediate Jacobian.
We check that our formulation and our results match with known ones under
various dimensional reductions, as well as comparing the holomorphic twist to
Kodaira-Spencer theory. Matching our formalism to five-dimensional Yang-Mills
theory after reduction leads to some issues related to electric-magnetic
duality; we offer some speculation on a nonperturbative resolution.
