Dans ce travail, nous étudions l’action du groupe d’automorphismes conformes d’une surface de Riemann de genre supérieur à deux sur ses structures spin. Nous caractérisons de telles surfaces qui admettent un automorphisme non-trivial fixant soit toutes les structures spin à la fois, soit seulement une. Les cas des courbes hyperelliptiques et de la quartique de Klein sont analysés en détail.
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.
@article{AFST_2010_6_19_3-4_457_0, author = {Kallel, Sadok and Sjerve, Denis}, title = {Invariant {Spin} {Structures} on {Riemann} {Surfaces}}, journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques}, pages = {457--477}, publisher = {Universit\'e Paul Sabatier, Institut de math\'ematiques}, address = {Toulouse}, volume = {Ser. 6, 19}, number = {3-4}, year = {2010}, doi = {10.5802/afst.1251}, zbl = {1213.14065}, mrnumber = {2790803}, language = {en}, url = {http://www.numdam.org/articles/10.5802/afst.1251/} }
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 SP - 457 EP - 477 VL - 19 IS - 3-4 PB - Université Paul Sabatier, Institut de mathématiques PP - Toulouse UR - http://www.numdam.org/articles/10.5802/afst.1251/ DO - 10.5802/afst.1251 LA - en ID - AFST_2010_6_19_3-4_457_0 ER -
%0 Journal Article %A Kallel, Sadok %A Sjerve, Denis %T Invariant Spin Structures on Riemann Surfaces %J Annales de la Faculté des sciences de Toulouse : Mathématiques %D 2010 %P 457-477 %V 19 %N 3-4 %I Université Paul Sabatier, Institut de mathématiques %C Toulouse %U http://www.numdam.org/articles/10.5802/afst.1251/ %R 10.5802/afst.1251 %G en %F AFST_2010_6_19_3-4_457_0
Kallel, Sadok; Sjerve, Denis. Invariant Spin Structures on Riemann Surfaces. Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 19 (2010) no. 3-4, pp. 457-477. doi : 10.5802/afst.1251. http://www.numdam.org/articles/10.5802/afst.1251/
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