Pathology of formal locally-trivial deformations in positive characteristic
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arXiv
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| Main Author: | |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866912760517885952 |
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| author | Miyamoto, Takuya |
| author_facet | Miyamoto, Takuya |
| contents | We construct explicit examples that are algebraic varieties in positive characteristic to show that locally trivial moduli functors do not always satisfy Schlessinger's condition $(H_1)$ in [3], in contrast to the complex/characteristic $0$ case. The first example is an algebraic curve, and the second is a normal rational projective surface with only one rational double point. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_00332 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Pathology of formal locally-trivial deformations in positive characteristic Miyamoto, Takuya Algebraic Geometry We construct explicit examples that are algebraic varieties in positive characteristic to show that locally trivial moduli functors do not always satisfy Schlessinger's condition $(H_1)$ in [3], in contrast to the complex/characteristic $0$ case. The first example is an algebraic curve, and the second is a normal rational projective surface with only one rational double point. |
| title | Pathology of formal locally-trivial deformations in positive characteristic |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2502.00332 |