Parity of the spin structure defined by a quadratic differential

Details Parity of the spin structure defined by a quadratic differential Parity of the spin structure defined by a quadratic differential

2002-10-08

arxiv.org/abs/math/0210116v2

Geom. Topol. 8(2004) 511-538

Mathematics

Geometric Topology

Published by Geometry and Topology at http://www.maths.warwick.ac.uk/gt/GTVol8/paper12.abs.html

Scientific paper

According to the work of Kontsevich-Zorich, the invariant that classifies non-hyperelliptic connected components of the moduli spaces of Abelian differentials with prescribed singularities,is the parity of the spin structure. We show that for the moduli space of quadratic differentials, the spin structure is constant on every stratum where it is defined. In particular this disproves the conjecture that it classifies the non-hyperelliptic connected components of the strata of quadratic differentials with prescribed singularities. An explicit formula for the parity of the spin structure is given.

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