The Picard group of the moduli space of r-Spin Riemann surfaces

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The Picard group of the moduli space of r-Spin Riemann surfaces. / Randal-Williams, Oscar.

I: Advances in Mathematics, Bind 231, Nr. 1, 2012, s. 482-515.

Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt

Harvard

Randal-Williams, O 2012, 'The Picard group of the moduli space of r-Spin Riemann surfaces', Advances in Mathematics, bind 231, nr. 1, s. 482-515. https://doi.org/10.1016/j.aim.2012.04.027

APA

Randal-Williams, O. (2012). The Picard group of the moduli space of r-Spin Riemann surfaces. Advances in Mathematics, 231(1), 482-515. https://doi.org/10.1016/j.aim.2012.04.027

Vancouver

Randal-Williams O. The Picard group of the moduli space of r-Spin Riemann surfaces. Advances in Mathematics. 2012;231(1):482-515. https://doi.org/10.1016/j.aim.2012.04.027

Author

Randal-Williams, Oscar. / The Picard group of the moduli space of r-Spin Riemann surfaces. I: Advances in Mathematics. 2012 ; Bind 231, Nr. 1. s. 482-515.

Bibtex

@article{977c4ff25b6a4e7498d6324228d86505,
title = "The Picard group of the moduli space of r-Spin Riemann surfaces",
abstract = "An r-Spin Riemann surface is a Riemann surface equipped with a choice of rth root of the (co)tangent bundle. We give a careful construction of the moduli space (orbifold) of r-Spin Riemann surfaces, and explain how to establish a Madsen–Weiss theorem for it. This allows us to prove the “Mumford conjecture” for these moduli spaces, but more interestingly allows us to compute their algebraic Picard groups (for g≥10, or g≥9 in the 2-Spin case). We give a complete description of these Picard groups, in terms of explicitly constructed line bundles.",
author = "Oscar Randal-Williams",
year = "2012",
doi = "10.1016/j.aim.2012.04.027",
language = "English",
volume = "231",
pages = "482--515",
journal = "Advances in Mathematics",
issn = "0001-8708",
publisher = "Academic Press",
number = "1",

}

RIS

TY - JOUR

T1 - The Picard group of the moduli space of r-Spin Riemann surfaces

AU - Randal-Williams, Oscar

PY - 2012

Y1 - 2012

N2 - An r-Spin Riemann surface is a Riemann surface equipped with a choice of rth root of the (co)tangent bundle. We give a careful construction of the moduli space (orbifold) of r-Spin Riemann surfaces, and explain how to establish a Madsen–Weiss theorem for it. This allows us to prove the “Mumford conjecture” for these moduli spaces, but more interestingly allows us to compute their algebraic Picard groups (for g≥10, or g≥9 in the 2-Spin case). We give a complete description of these Picard groups, in terms of explicitly constructed line bundles.

AB - An r-Spin Riemann surface is a Riemann surface equipped with a choice of rth root of the (co)tangent bundle. We give a careful construction of the moduli space (orbifold) of r-Spin Riemann surfaces, and explain how to establish a Madsen–Weiss theorem for it. This allows us to prove the “Mumford conjecture” for these moduli spaces, but more interestingly allows us to compute their algebraic Picard groups (for g≥10, or g≥9 in the 2-Spin case). We give a complete description of these Picard groups, in terms of explicitly constructed line bundles.

U2 - 10.1016/j.aim.2012.04.027

DO - 10.1016/j.aim.2012.04.027

M3 - Journal article

VL - 231

SP - 482

EP - 515

JO - Advances in Mathematics

JF - Advances in Mathematics

SN - 0001-8708

IS - 1

ER -

ID: 49698935