Let V be a chiral algebra (associated to a vertex algebra) over a family X of complex curves.
An important collection of objects associated to V are the spaces of conformal blocks.
Roughly speaking these are spaces of sections of V over fibres, whose dependence on the
moduli yields a bundle with flat connection over the family. Understanding the structure of
conformal blocks in particular cases leads to interesting theorems. Examples include
nonabelian theta functions, and Zhu's theorem on modular invariance of vertex algebra characters.

In this talk I will describe joint work with R. Heluani in which we construct superconformal
blocks associated to N=2 SUSY vertex algebras living on super-analogues of elliptic curves.
The family of supercurves is described as a quotient by the classical Jacobi group,
and equivariance of normalised superconformal blocks under this group establishes their
transformation under this group as Jacobi forms.