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arXiv · 2603.06083

The map to the orbifold base need not be an orbifold map

Finn Bartsch
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Abstract

We give an explicit example of a fibration $f \colon X \to Y$ between smooth projective varieties whose "orbifold base" $\Delta_f$ in the sense of Campana has the property that the induced morphism $X \to (Y, \Delta_f)$ 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 $(Y, \Delta_f)$ 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.

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Finn Bartsch. 2026-03-06. The map to the orbifold base need not be an orbifold map. https://arxiv.org/abs/2603.06083

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