Moduli spaces of Riemann surfaces as Hurwitz spaces

Institut for Matematiske Fag

Moduli spaces of Riemann surfaces as Hurwitz spaces

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Standard

Moduli spaces of Riemann surfaces as Hurwitz spaces. / Bianchi, Andrea.

I: Advances in Mathematics, Bind 430, 109217, 2023.

Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt

Harvard

Bianchi, A 2023, 'Moduli spaces of Riemann surfaces as Hurwitz spaces', Advances in Mathematics, bind 430, 109217. https://doi.org/10.1016/j.aim.2023.109217

APA

Bianchi, A. (2023). Moduli spaces of Riemann surfaces as Hurwitz spaces. Advances in Mathematics, 430, [109217]. https://doi.org/10.1016/j.aim.2023.109217

Vancouver

Bianchi A. Moduli spaces of Riemann surfaces as Hurwitz spaces. Advances in Mathematics. 2023;430. 109217. https://doi.org/10.1016/j.aim.2023.109217

Author

Bianchi, Andrea. / Moduli spaces of Riemann surfaces as Hurwitz spaces. I: Advances in Mathematics. 2023 ; Bind 430.

Bibtex

@article{01969c795b484007ae3275c462a72d9f,

title = "Moduli spaces of Riemann surfaces as Hurwitz spaces",

abstract = "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.",

keywords = "Group completion, Hurwitz space, Moduli space, Riemann-Roch",

author = "Andrea Bianchi",

note = "Publisher Copyright: {\textcopyright} 2023 Elsevier Inc.",

year = "2023",

doi = "10.1016/j.aim.2023.109217",

language = "English",

volume = "430",

journal = "Advances in Mathematics",

issn = "0001-8708",

publisher = "Academic Press",

}

RIS

TY - JOUR

T1 - Moduli spaces of Riemann surfaces as Hurwitz spaces

AU - Bianchi, Andrea

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