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arXiv · 2405.12620

On the smoothability problem with rational coefficients

Olivier Benoist·Claire Voisin
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Abstract

We consider the problem of smoothing algebraic cycles with rational coefficients on smooth projective complex varieties up to homological equivalence. We show that a solution to this problem would be incompatible with the validity of the Hartshorne conjecture on complete intersections in projective space. We also solve unconditionally a symplectic variant of this problem.

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Olivier Benoist, Claire Voisin. 2024-05-21. On the smoothability problem with rational coefficients. https://arxiv.org/abs/2405.12620

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