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Parity of the spin structure defined by a quadratic differential. (English) Zbl 1064.32010
The spin structure of the moduli space of quadratic differentials on a Riemann surface is studied. It is shown that this spin structure is constant on every stratum where it is defined. This disproves a conjecture that the spin structure classifies the non-hyperelliptic components of the strata of quadratic differentials. The parity of the spin structure is given in explicit form.

##### MSC:
 32G15 Moduli of Riemann surfaces, Teichmüller theory (complex-analytic aspects in several variables) 30F30 Differentials on Riemann surfaces 57R15 Specialized structures on manifolds (spin manifolds, framed manifolds, etc.)
##### Keywords:
quadratic differentials; moduli spaces; spin structure
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##### References:
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