Terminal singularities of the moduli space of curves on low degree hypersurfaces and the circle method
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866917878303817728 |
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| author | Glas, Jakob Hase-Liu, Matthew |
| author_facet | Glas, Jakob Hase-Liu, Matthew |
| contents | We study the singularities of the moduli space of degree $e$ maps from smooth genus $g$ curves to an arbitrary smooth hypersurface of low degree. For $e$ large compared to $g$, we show that these moduli spaces have at worst terminal singularities. Our main approach is to study the jet schemes of these moduli spaces by developing a suitable form of the circle method. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_14923 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Terminal singularities of the moduli space of curves on low degree hypersurfaces and the circle method Glas, Jakob Hase-Liu, Matthew Algebraic Geometry Number Theory 14H10 (11D45, 11P55, 14G05, 14J70) We study the singularities of the moduli space of degree $e$ maps from smooth genus $g$ curves to an arbitrary smooth hypersurface of low degree. For $e$ large compared to $g$, we show that these moduli spaces have at worst terminal singularities. Our main approach is to study the jet schemes of these moduli spaces by developing a suitable form of the circle method. |
| title | Terminal singularities of the moduli space of curves on low degree hypersurfaces and the circle method |
| topic | Algebraic Geometry Number Theory 14H10 (11D45, 11P55, 14G05, 14J70) |
| url | https://arxiv.org/abs/2412.14923 |