JournalsrlmVol. 36, No. 3pp. 393–408

On the smoothability problem with rational coefficients

  • Olivier Benoist

    École Normale Supérieure et CNRS, Paris, France

  • Claire Voisin

    Institut de Mathématiques de Jussieu-Paris Rive Gauche et CNRS, Paris, France
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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.

Cite this article

Olivier Benoist, Claire Voisin, On the smoothability problem with rational coefficients. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. 36 (2025), no. 3, pp. 393–408

DOI 10.4171/RLM/1076