The Picard group of the universal moduli stack of principal bundles on pointed smooth curves II

In this paper, which is a sequel of [14], we investigate, for any reductive group G over an algebraically closed field k, the Picard group of the universal moduli stack BunG;g;n of G-bundles over n-pointed smooth projective curves of genus g. In particular, we give new functorial presentations of the Picard group of BunG;g;n, we study the restriction homomorphism onto the Picard group of the moduli stack of principal G-bundles over a fixed smooth curve, we determine the Picard group of the rigidification of BunG;g;n by the center of G as well as the image of the obstruction homomorphism of the associated gerbe. As a consequence, we compute the divisor class group of the moduli space of semistable G-bundles over n-pointed smooth projective curves of genus g.