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 , p. 457-477
MR 2790803 | Zbl 1213.14065
doi : 10.5802/afst.1251
URL stable : http://www.numdam.org/item?id=AFST_2010_6_19_3-4_457_0

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.

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