Stable cohomology of the universal Picard varieties and the extended mapping class group
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Stable cohomology of the universal Picard varieties and the extended mapping class group. / Ebert, Johannes; Randal-Williams, Oscar.
I: Documenta Mathematica, Bind 17, 2012, s. 417-450.Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt
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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