The map to the orbifold base need not be an orbifold map
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866910043544223744 |
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| author | Bartsch, Finn |
| author_facet | Bartsch, Finn |
| contents | We give an explicit example of a fibration $f \colon X \to Y$ between smooth projective varieties whose "orbifold base" $Δ_f$ in the sense of Campana has the property that the induced morphism $X \to (Y, Δ_f)$ is not a morphism of C-pairs (i.e., it is not an "orbifold morphism"). We however also show that this cannot happen if $f$ is "neat" and $(Y, Δ_f)$ is sufficiently well-behaved. Finally, we discuss the implications of this statement towards conjectures of Campana aiming to give algebro-geometric characterizations of those varieties which either admit a dense entire curve or a potentially dense set of integral points. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_06083 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The map to the orbifold base need not be an orbifold map Bartsch, Finn Algebraic Geometry 14E22 (Primary) 14G05, 32Q45 (Secondary) We give an explicit example of a fibration $f \colon X \to Y$ between smooth projective varieties whose "orbifold base" $Δ_f$ in the sense of Campana has the property that the induced morphism $X \to (Y, Δ_f)$ is not a morphism of C-pairs (i.e., it is not an "orbifold morphism"). We however also show that this cannot happen if $f$ is "neat" and $(Y, Δ_f)$ is sufficiently well-behaved. Finally, we discuss the implications of this statement towards conjectures of Campana aiming to give algebro-geometric characterizations of those varieties which either admit a dense entire curve or a potentially dense set of integral points. |
| title | The map to the orbifold base need not be an orbifold map |
| topic | Algebraic Geometry 14E22 (Primary) 14G05, 32Q45 (Secondary) |
| url | https://arxiv.org/abs/2603.06083 |