Geodesic
Stable cohomology of the universal Picard varieties and the extended mapping class group
Documenta mathematica, Tome 17 (2012), pp. 417-450
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We study the moduli spaces which classify smooth surfaces along with a complex line bundle. There are homological stability and Madsen–Weiss type results for these spaces (mostly due to Cohen and Madsen), and we discuss the cohomological calculations which may be deduced from them. We then relate these spaces to (a generalisation of) Kawazumi's extended mapping class groups, and hence deduce cohomological information about these. Finally, we relate these results to complex algebraic geometry. We construct a holomorphic stack classifying families of Riemann surfaces equipped with a fibrewise holomorphic line bundle, which is a gerbe over the universal Picard variety, and compute its holomorphic Picard group.
DOI : 10.4171/dm/371
Classification : 14C22, 14H15, 32G15, 55R40, 57R20
Mots-clés : moduli spaces, Picard variety, stable cohomology 
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     author = {Johannes Ebert and Oscar Randal-Williams},
     title = {Stable cohomology of the universal {Picard} varieties and the extended mapping class group},
     journal = {Documenta mathematica},
     pages = {417--450},
     year = {2012},
     volume = {17},
     doi = {10.4171/dm/371},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/371/}
}
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Johannes Ebert; Oscar Randal-Williams. Stable cohomology of the universal Picard varieties and the extended mapping class group. Documenta mathematica, Tome 17 (2012), pp. 417-450. doi: 10.4171/dm/371

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