Stable cohomology of the universal Picard varieties and the extended mapping class group

Research output: Contribution to journal › Journal article › Research › peer-review

Standard

Stable cohomology of the universal Picard varieties and the extended mapping class group. / Ebert, Johannes; Randal-Williams, Oscar.

In: Documenta Mathematica, Vol. 17, 2012, p. 417-450.

Research output: Contribution to journal › Journal article › Research › peer-review

Harvard

Ebert, J & Randal-Williams, O 2012, 'Stable cohomology of the universal Picard varieties and the extended mapping class group', Documenta Mathematica, vol. 17, pp. 417-450.

APA

Ebert, J., & Randal-Williams, O. (2012). Stable cohomology of the universal Picard varieties and the extended mapping class group. Documenta Mathematica, 17, 417-450.

Vancouver

Ebert J, Randal-Williams O. Stable cohomology of the universal Picard varieties and the extended mapping class group. Documenta Mathematica. 2012;17:417-450.

Author

Ebert, Johannes ; Randal-Williams, Oscar. / Stable cohomology of the universal Picard varieties and the extended mapping class group. In: Documenta Mathematica. 2012 ; Vol. 17. pp. 417-450.

Bibtex

@article{afb1254b3e804ff884d5f985e4c41345,
title = "Stable cohomology of the universal Picard varieties and the extended mapping class group",
abstract = "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. ",
author = "Johannes Ebert and Oscar Randal-Williams",
year = "2012",
language = "English",
volume = "17",
pages = "417--450",
journal = "Documenta Mathematica",
issn = "1431-0635",
publisher = "Deutsche Mathematiker Vereinigung",

}

RIS

TY - JOUR

T1 - Stable cohomology of the universal Picard varieties and the extended mapping class group

AU - Ebert, Johannes

AU - Randal-Williams, Oscar

PY - 2012

Y1 - 2012

N2 - 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.

AB - 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.

M3 - Journal article

VL - 17

SP - 417

EP - 450

JO - Documenta Mathematica

JF - Documenta Mathematica

SN - 1431-0635

ER -

ID: 117372358