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arXiv · 2604.07876

The parity of theta characteristics is preserved by infinitesimal deformations

Margarida Mendes Lopes·Rita Pardini·Roberto Pignatelli
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Abstract

In this note, given a family of relative dimension one over a smooth curve, we determine the parity of the restriction of a relative theta characteristic to an arbitrary multiple of a fiber in terms of the parity of the restriction to a general fibre. This result can be regarded as a variant of the well-known theorem on the invariance of the parity of theta characteristics in families. As a corollary, we obtain that the torsion subsheaf of the first higher direct image sheaf of a relative theta characteristic splits as a direct sum of two isomorphic sheaves.

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Margarida Mendes Lopes, Rita Pardini, Roberto Pignatelli. 2026-04-16. The parity of theta characteristics is preserved by infinitesimal deformations. https://arxiv.org/abs/2604.07876

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