Picard group of moduli of hyperelliptic curves

Abstract

The main subject of this work is the difference between the coarse moduli space and the stack of hyperelliptic curves. We compute their Picard groups, giving explicit description of the generators. We get an application to the (non-)existence of a tautological family over the coarse moduli space.

13 pages. Section 2 has been shortened and the final appendix has been erased. Final version, to appear on Math. Zeit