We treat the problem of completing the moduli space for roots of line bundles on curves. Special attention is devoted to higher spin curves within the universal Picard scheme. Two new different constructions, both using line bundles on nodal curves as boundary points, are carried out and compared with pre-existing ones.
Caporaso, L., Casagrande, C., Cornalba, M. (2007). Moduli of roots of line bundles on curves. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 359(8), 3733-3768.