Geodesic
Stable cohomology of the universal Picard varieties and the extended mapping class group
Documenta mathematica, Tome 17 (2012), pp. 417-450.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: 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.
Classification : 14H15, 32G15, 14C22, 57R20, 55R40
Keywords: moduli spaces, Picard variety, stable cohomology 
@article{DOCMA_2012__17__a17,
     author = {Ebert, Johannes and Randal-Williams, Oscar},
     title = {Stable cohomology of the universal {Picard} varieties and the extended mapping class group},
     journal = {Documenta mathematica},
     pages = {417--450},
     publisher = {mathdoc},
     volume = {17},
     year = {2012},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DOCMA_2012__17__a17/}
}
TY  - JOUR
AU  - Ebert, Johannes
AU  - Randal-Williams, Oscar
TI  - Stable cohomology of the universal Picard varieties and the extended mapping class group
JO  - Documenta mathematica
PY  - 2012
SP  - 417
EP  - 450
VL  - 17
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DOCMA_2012__17__a17/
LA  - en
ID  - DOCMA_2012__17__a17
ER  - 
%0 Journal Article
%A Ebert, Johannes
%A Randal-Williams, Oscar
%T Stable cohomology of the universal Picard varieties and the extended mapping class group
%J Documenta mathematica
%D 2012
%P 417-450
%V 17
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DOCMA_2012__17__a17/
%G en
%F DOCMA_2012__17__a17
Ebert, Johannes; Randal-Williams, Oscar. Stable cohomology of the universal Picard varieties and the extended mapping class group. Documenta mathematica, Tome 17 (2012), pp. 417-450. http://geodesic.mathdoc.fr/item/DOCMA_2012__17__a17/