Moduli spaces of Riemann surfaces as Hurwitz spaces
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Moduli spaces of Riemann surfaces as Hurwitz spaces. / Bianchi, Andrea.
In: Advances in Mathematics, Vol. 430, 109217, 2023.Research output: Contribution to journal › Journal article › Research › peer-review
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TY - JOUR
T1 - Moduli spaces of Riemann surfaces as Hurwitz spaces
AU - Bianchi, Andrea
N1 - Publisher Copyright: © 2023 Elsevier Inc.
PY - 2023
Y1 - 2023
N2 - We consider the moduli space Mg,n of Riemann surfaces of genus g≥0 with n≥1 ordered and directed marked points. For d≥2g+n−1 we show that Mg,n is homotopy equivalent to a component of the simplicial Hurwitz space HurΔ(Sdgeo) associated with the partially multiplicative quandle Sdgeo. As an application, we give a new proof of the Mumford conjecture on the stable rational cohomology of moduli spaces of Riemann surfaces. We also provide a combinatorial model for the infinite loop space Ω∞−2MTSO(2) of Hurwitz flavour.
AB - We consider the moduli space Mg,n of Riemann surfaces of genus g≥0 with n≥1 ordered and directed marked points. For d≥2g+n−1 we show that Mg,n is homotopy equivalent to a component of the simplicial Hurwitz space HurΔ(Sdgeo) associated with the partially multiplicative quandle Sdgeo. As an application, we give a new proof of the Mumford conjecture on the stable rational cohomology of moduli spaces of Riemann surfaces. We also provide a combinatorial model for the infinite loop space Ω∞−2MTSO(2) of Hurwitz flavour.
KW - Group completion
KW - Hurwitz space
KW - Moduli space
KW - Riemann-Roch
U2 - 10.1016/j.aim.2023.109217
DO - 10.1016/j.aim.2023.109217
M3 - Journal article
AN - SCOPUS:85165687897
VL - 430
JO - Advances in Mathematics
JF - Advances in Mathematics
SN - 0001-8708
M1 - 109217
ER -
ID: 369246681