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Mosc. Math. J., 2016, Volume 16, Number 1, Pages 95–124 (Mi mmj595)  

This article is cited in 1 scientific paper (total in 1 paper)

Higher spin Klein surfaces

Sergey Natanzonab, Anna Pratoussevitchc

a Institute of Theoretical and Experimental Physics (ITEP), Moscow, Russia
b National Research University Higher School of Economics, Vavilova Street 7, 117312 Moscow, Russia
c Department of Mathematical Sciences, University of Liverpool, Liverpool L69 7ZL

Abstract: A Klein surface is a generalisation of a Riemann surface to the case of non-orientable surfaces or surfaces with boundary. The category of Klein surfaces is isomorphic to the category of real algebraic curves. An $m$-spin structure on a Klein surface is a complex line bundle whose $m$-th tensor power is the cotangent bundle. We describe all $m$-spin structures on Klein surfaces of genus greater than one and determine the conditions for their existence. In particular we compute the number of $m$-spin structures on a Klein surface in terms of its natural topological invariants.

Key words and phrases: higher spin bundles, higher Theta characteristics, real forms, Riemann surfaces, Klein surfaces, Arf functions, lifts of Fuchsian groups.

Funding Agency Grant Number
National Research University Higher School of Economics 15-01-0052
Ministry of Education and Science of the Russian Federation
Leverhulme Trust RPG-057
Grant support for S.N.: The article was prepared within the framework of the Academic Fund Program at the National Research University Higher School of Economics (HSE) in 2015–16 (grant Nr. 15-01-0052) and supported within the framework of a subsidy granted to the HSE by the Government of the Russian Federation for the implementation of the Global Competitiveness Program.
Grant support for A.P.: The work was supported in part by the Leverhulme Trust grant RPG-057.


DOI: https://doi.org/10.17323/1609-4514-2016-16-1-95-124

Full text: http://www.mathjournals.org/.../2016-016-001-004.html
References: PDF file   HTML file

Bibliographic databases:

MSC: Primary 30F50, 14H60, 30F35; Secondary 30F60
Received: February 25, 2015; in revised form July 27, 2015
Language:

Citation: Sergey Natanzon, Anna Pratoussevitch, “Higher spin Klein surfaces”, Mosc. Math. J., 16:1 (2016), 95–124

Citation in format AMSBIB
\Bibitem{NatPra16}
\by Sergey~Natanzon, Anna~Pratoussevitch
\paper Higher spin Klein surfaces
\jour Mosc. Math.~J.
\yr 2016
\vol 16
\issue 1
\pages 95--124
\mathnet{http://mi.mathnet.ru/mmj595}
\crossref{https://doi.org/10.17323/1609-4514-2016-16-1-95-124}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3470577}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000386360200004}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Sergey Natanzon, Anna Pratoussevitch, “Moduli spaces of higher spin Klein surfaces”, Mosc. Math. J., 17:2 (2017), 327–349  mathnet  mathscinet
  • Moscow Mathematical Journal
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