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arXiv · 2608.23021

On smooth affine surfaces with the cohomology of a smooth projective curve

Arnab Roy
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Abstract

We prove that if a smooth affine complex surface has the same rational mixed Hodge structure as a smooth projective curve of positive genus, then it admits a smooth morphism to the curve with fibers isomorphic to affine line. In particular, every such surface is the total space of a torsor for a line bundle on the curve. The motivation comes from Jouanolou's trick, to which this result gives a kind of converse in dimension 2.

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Arnab Roy. 2026-08-24. On smooth affine surfaces with the cohomology of a smooth projective curve. https://arxiv.org/abs/2608.23021

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