Picard group of the compactified universal Picard stack

Details Picard group of the compactified universal Picard stack Picard group of the compactified universal Picard stack

2010-07-26

arxiv.org/abs/1007.4519v3

Mathematics

Algebraic Geometry

35 pages. Major revision: we give explicit generators for the Picard group using the formalism of the determinant of cohomolog

Scientific paper

We compute the Picard groups of the universal Picard stack over the stack of smooth curves and of its compactification over the stack of stable curves. Along the way, we prove some results concerning the gerbe structure of the universal Picard stack over its rigidification by the natural action of the multiplicative group and relate this with the existence of generalized Poincar\'e line bundles. We also compare our results with Kouvidakis-Fontanari computations of the Picard group of the universal (compactified) Picard scheme.

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