### Metadata

### Abstract

Let $\varphi $ be a $\mathbb{Z}/2\mathbb{Z}$-spin structure on a closed oriented surface ${\Sigma}_{g}$ of genus $g\ge 4$. We determine a generating set of the stabilizer of $\varphi $ in the mapping class group of ${\Sigma}_{g}$ consisting of Dehn twists about an explicit collection of $2g+1$ curves on ${\Sigma}_{g}$. If $g=3$ then we determine a generating set of the stabilizer of an odd $\mathbb{Z}/4\mathbb{Z}$-spin structure consisting of Dehn twists about a collection of $6$ curves.

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