On the Berezinian of a moduli space of curves in P^{n|n+1}

Abstract

A supermanifold P^{3|4} is a target space for twistor string theory. In this note we identify a line bundle of holomorphic volume elements BerM_gP^{3|4} defined on the moduli space of curves of genus g in P^{3|4} with a pullback of a line bundle defined on M_g(pt). We also give some generalizations of this fact.