Invariant Spin Structures on Riemann Surfaces

Sadok Kallel[1]; Denis Sjerve[2]

  • [1] Laboratoire Painlevé, Université de Lille I, France
  • [2] Department of Mathematics, University of British Columbia,Canada

Annales de la faculté des sciences de Toulouse Mathématiques (2010)

  • Volume: 19, Issue: 3-4, page 457-477
  • ISSN: 0240-2963

Abstract

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We investigate the action of the automorphism group of a closed Riemann surface of genus at least two on its set of theta characteristics (or spin structures). We give a characterization of those surfaces admitting a non-trivial automorphism fixing either all of the spin structures or just one. The case of hyperelliptic curves and of the Klein quartic are discussed in detail.

How to cite

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Kallel, Sadok, and Sjerve, Denis. "Invariant Spin Structures on Riemann Surfaces." Annales de la faculté des sciences de Toulouse Mathématiques 19.3-4 (2010): 457-477. <http://eudml.org/doc/115891>.

@article{Kallel2010,
abstract = {We investigate the action of the automorphism group of a closed Riemann surface of genus at least two on its set of theta characteristics (or spin structures). We give a characterization of those surfaces admitting a non-trivial automorphism fixing either all of the spin structures or just one. The case of hyperelliptic curves and of the Klein quartic are discussed in detail.},
affiliation = {Laboratoire Painlevé, Université de Lille I, France; Department of Mathematics, University of British Columbia,Canada},
author = {Kallel, Sadok, Sjerve, Denis},
journal = {Annales de la faculté des sciences de Toulouse Mathématiques},
language = {eng},
number = {3-4},
pages = {457-477},
publisher = {Université Paul Sabatier, Toulouse},
title = {Invariant Spin Structures on Riemann Surfaces},
url = {http://eudml.org/doc/115891},
volume = {19},
year = {2010},
}

TY - JOUR
AU - Kallel, Sadok
AU - Sjerve, Denis
TI - Invariant Spin Structures on Riemann Surfaces
JO - Annales de la faculté des sciences de Toulouse Mathématiques
PY - 2010
PB - Université Paul Sabatier, Toulouse
VL - 19
IS - 3-4
SP - 457
EP - 477
AB - We investigate the action of the automorphism group of a closed Riemann surface of genus at least two on its set of theta characteristics (or spin structures). We give a characterization of those surfaces admitting a non-trivial automorphism fixing either all of the spin structures or just one. The case of hyperelliptic curves and of the Klein quartic are discussed in detail.
LA - eng
UR - http://eudml.org/doc/115891
ER -

References

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  12. Mumford (D.).— Theta characteristics of an algebraic curve, Ann. Sci. École Norm. Sup. (4) 4 (1971), p. 181-192. Zbl0216.05904MR292836
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