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Pré-Publication, Document De Travail Année : 2023

Flat pushforwards of Chern classes and the smoothing problem for cycles in the Whitney range

Résumé

We investigate the smoothability of cycles in the Whitney range, that is, when the dimension is strictly smaller than the codimension. Introducing the notion of ``flat pushforwards of Chern classes" and studying its properties, we prove that cycles of dimension $d\leq 7$ are smoothable in a smooth variety of dimension $>2d$, and more generally that $(d-6)!Z$, $d={\rm dim}\,Z$, is smoothable in a variety of dimension $>2d$. We also prove that cycles of any dimension on homogeneous varieties are smoothable in the Whitney range. We prove more generally in all these cases that the considered cycles are flat pushforwards of intersections of divisors on a smooth projective variety.
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Dates et versions

hal-04275935 , version 1 (08-11-2023)

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  • HAL Id : hal-04275935 , version 1

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Claire Voisin. Flat pushforwards of Chern classes and the smoothing problem for cycles in the Whitney range. 2023. ⟨hal-04275935⟩
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