The parity of theta characteristics is preserved by infinitesimal deformations
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866908969397649408 |
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| author | Lopes, Margarida Mendes Pardini, Rita Pignatelli, Roberto |
| author_facet | Lopes, Margarida Mendes Pardini, Rita Pignatelli, Roberto |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_07876 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The parity of theta characteristics is preserved by infinitesimal deformations Lopes, Margarida Mendes Pardini, Rita Pignatelli, Roberto Algebraic Geometry 14H10 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. |
| title | The parity of theta characteristics is preserved by infinitesimal deformations |
| topic | Algebraic Geometry 14H10 |
| url | https://arxiv.org/abs/2604.07876 |