We will introduce and discuss a notion of s-fractional mass for 1-currents, generalizing the s-fractional perimeter in the plane to higher codimension singularities. We will present basic compactness and density properties for such a notion, and discuss possible future directions of investigation. This is a joint work with M. Cicalese, T. Heilmann, A. Kubin and F. Onoue. This seminar is part of the activities of the Dipartimento di Eccellenza CUP B83C23001390001 and it is funded by the European Union – Next Generation EU.