The supermoduli space of genus zero super Riemann surfaces with Ramond punctures

Nadia Ott; Alexander A. Voronov

doi:10.1016/j.geomphys.2022.104726

The supermoduli space of genus zero super Riemann surfaces with Ramond punctures

Nadia Ott, Alexander A. Voronov

School of Mathematics

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

We give an explicit quotient description of the (n_R−3|n_R/2−2)-dimensional supermoduli space M_{0,n_R} of genus zero super Riemann surfaces with n_R≥4 Ramond punctures and prove that it is a Deligne-Mumford superstack. We also give an explicit quotient description of the supermoduli stack of genus zero supercurves with no SUSY structure.

Original language	English (US)
Article number	104726
Journal	Journal of Geometry and Physics
Volume	185
DOIs	https://doi.org/10.1016/j.geomphys.2022.104726
State	Published - Mar 2023

Bibliographical note

Funding Information:
We are grateful to Christine Berkesch, Ugo Bruzzo, Ionuţ Ciocan-Fontanine, Giulio Codogni, Daniel J. Diroff, Ron Donagi, Rita Fioresi, and Daniel Hernández Ruipérez for helpful discussions. N. O. thanks the Mittag-Leffler Institute and the Centre for Quantum Mathematics as the University of Southern Denmark for hospitality at various stages of work on the project. A. A. V. expresses his gratitude to New York University Abu Dhabi for hospitality during his sabbatical in 2019. The work of the first author was supported by the Simons Postdoctoral grant at the University of Pennsylvania. The work of the second author was supported by World Premier International Research Center Initiative (WPI), MEXT, Japan, and a Collaboration grant from the Simons Foundation (#585720).

Funding Information:
We are grateful to Christine Berkesch, Ugo Bruzzo, Ionuţ Ciocan-Fontanine, Giulio Codogni, Daniel J. Diroff, Ron Donagi, Rita Fioresi, and Daniel Hernández Ruipérez for helpful discussions. N. O. thanks the Mittag-Leffler Institute and the Centre for Quantum Mathematics as the University of Southern Denmark for hospitality at various stages of work on the project. A. A. V. expresses his gratitude to New York University Abu Dhabi for hospitality during his sabbatical in 2019. The work of the first author was supported by the Simons Postdoctoral grant at the University of Pennsylvania . The work of the second author was supported by World Premier International Research Center Initiative (WPI), MEXT , Japan, and a Collaboration grant from the Simons Foundation (# 585720 ).

Publisher Copyright:
© 2022 Elsevier B.V.

Keywords

Ramond punctures
Super Riemann surfaces
Supermoduli space

Publisher link

10.1016/j.geomphys.2022.104726

Find It

Find It at U of M Libraries

Cite this

@article{0d9930f4cbe646ea930bacc370f383b4,

title = "The supermoduli space of genus zero super Riemann surfaces with Ramond punctures",

abstract = "We give an explicit quotient description of the (nR−3|nR/2−2)-dimensional supermoduli space M0,nR of genus zero super Riemann surfaces with nR≥4 Ramond punctures and prove that it is a Deligne-Mumford superstack. We also give an explicit quotient description of the supermoduli stack of genus zero supercurves with no SUSY structure.",

keywords = "Ramond punctures, Super Riemann surfaces, Supermoduli space",

author = "Nadia Ott and Voronov, {Alexander A.}",

note = "Funding Information: We are grateful to Christine Berkesch, Ugo Bruzzo, Ionu{\c t} Ciocan-Fontanine, Giulio Codogni, Daniel J. Diroff, Ron Donagi, Rita Fioresi, and Daniel Hern{\'a}ndez Ruip{\'e}rez for helpful discussions. N. O. thanks the Mittag-Leffler Institute and the Centre for Quantum Mathematics as the University of Southern Denmark for hospitality at various stages of work on the project. A. A. V. expresses his gratitude to New York University Abu Dhabi for hospitality during his sabbatical in 2019. The work of the first author was supported by the Simons Postdoctoral grant at the University of Pennsylvania. The work of the second author was supported by World Premier International Research Center Initiative (WPI), MEXT, Japan, and a Collaboration grant from the Simons Foundation (#585720). Funding Information: We are grateful to Christine Berkesch, Ugo Bruzzo, Ionu{\c t} Ciocan-Fontanine, Giulio Codogni, Daniel J. Diroff, Ron Donagi, Rita Fioresi, and Daniel Hern{\'a}ndez Ruip{\'e}rez for helpful discussions. N. O. thanks the Mittag-Leffler Institute and the Centre for Quantum Mathematics as the University of Southern Denmark for hospitality at various stages of work on the project. A. A. V. expresses his gratitude to New York University Abu Dhabi for hospitality during his sabbatical in 2019. The work of the first author was supported by the Simons Postdoctoral grant at the University of Pennsylvania . The work of the second author was supported by World Premier International Research Center Initiative (WPI), MEXT , Japan, and a Collaboration grant from the Simons Foundation (# 585720 ). Publisher Copyright: {\textcopyright} 2022 Elsevier B.V.",

year = "2023",

month = mar,

doi = "10.1016/j.geomphys.2022.104726",

language = "English (US)",

volume = "185",

journal = "Journal of Geometry and Physics",

issn = "0393-0440",

publisher = "Elsevier",

}

TY - JOUR

T1 - The supermoduli space of genus zero super Riemann surfaces with Ramond punctures

AU - Ott, Nadia

AU - Voronov, Alexander A.

N1 - Funding Information: We are grateful to Christine Berkesch, Ugo Bruzzo, Ionuţ Ciocan-Fontanine, Giulio Codogni, Daniel J. Diroff, Ron Donagi, Rita Fioresi, and Daniel Hernández Ruipérez for helpful discussions. N. O. thanks the Mittag-Leffler Institute and the Centre for Quantum Mathematics as the University of Southern Denmark for hospitality at various stages of work on the project. A. A. V. expresses his gratitude to New York University Abu Dhabi for hospitality during his sabbatical in 2019. The work of the first author was supported by the Simons Postdoctoral grant at the University of Pennsylvania. The work of the second author was supported by World Premier International Research Center Initiative (WPI), MEXT, Japan, and a Collaboration grant from the Simons Foundation (#585720). Funding Information: We are grateful to Christine Berkesch, Ugo Bruzzo, Ionuţ Ciocan-Fontanine, Giulio Codogni, Daniel J. Diroff, Ron Donagi, Rita Fioresi, and Daniel Hernández Ruipérez for helpful discussions. N. O. thanks the Mittag-Leffler Institute and the Centre for Quantum Mathematics as the University of Southern Denmark for hospitality at various stages of work on the project. A. A. V. expresses his gratitude to New York University Abu Dhabi for hospitality during his sabbatical in 2019. The work of the first author was supported by the Simons Postdoctoral grant at the University of Pennsylvania . The work of the second author was supported by World Premier International Research Center Initiative (WPI), MEXT , Japan, and a Collaboration grant from the Simons Foundation (# 585720 ). Publisher Copyright: © 2022 Elsevier B.V.

PY - 2023/3

Y1 - 2023/3

N2 - We give an explicit quotient description of the (nR−3|nR/2−2)-dimensional supermoduli space M0,nR of genus zero super Riemann surfaces with nR≥4 Ramond punctures and prove that it is a Deligne-Mumford superstack. We also give an explicit quotient description of the supermoduli stack of genus zero supercurves with no SUSY structure.

AB - We give an explicit quotient description of the (nR−3|nR/2−2)-dimensional supermoduli space M0,nR of genus zero super Riemann surfaces with nR≥4 Ramond punctures and prove that it is a Deligne-Mumford superstack. We also give an explicit quotient description of the supermoduli stack of genus zero supercurves with no SUSY structure.

KW - Ramond punctures

KW - Super Riemann surfaces

KW - Supermoduli space

UR - http://www.scopus.com/inward/record.url?scp=85145685123&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85145685123&partnerID=8YFLogxK

U2 - 10.1016/j.geomphys.2022.104726

DO - 10.1016/j.geomphys.2022.104726

M3 - Article

AN - SCOPUS:85145685123

SN - 0393-0440

VL - 185

JO - Journal of Geometry and Physics

JF - Journal of Geometry and Physics

M1 - 104726

ER -

The supermoduli space of genus zero super Riemann surfaces with Ramond punctures

Abstract

Bibliographical note

Keywords

Publisher link

Find It

Other files and links

Fingerprint

Cite this