abstract: We explain how to construct conformal blocks over superelliptic curves associated to topologically twisted N=2 SUSY vertex algebras. The geometry of the moduli space of such supercurves leads to a natural action of the Jacobi group \(SL(2, \mathbb{Z}) \times \mathbb{Z}^2\) which, in the presence of some regularity conditions on the vertex algebra, implies Jacobi invariance of its characters.