The Picard group of the compactified universal Jacobian

摘要

We determine explicitly the Picard groups of the universal Jacobian stack andof its compactification over the stack of stable curves. Along the way, weprove some results concerning the gerbe structure of the universal Jacobianstack over its rigidification by the natural action of the multiplicative groupand relate this with the existence of generalized Poincar\'e line bundles. Wealso compare our results with Kouvidakis-Fontanari computations of the divisorclass group of the universal (compactified) Jacobian scheme.