Factorization and modular invariance of multi-loop superstring amplitudes in the unitary gauge

We investigate the compatibility of unitary gauges in covariant fermionic strings with multi-loop modular invariance and factorization. Earlier objections regarding modular invariance disappear since arbitrary reference spin structures are admissible. The physical factorization hypothesis is confirmed, and a subclass of gauges is identified which factorizes bosonic amplitudes in the 'zero' picture alone. Details are worked out explicitly in a two-loop example. (orig.)