01:47:04
publiée le 10 mai 2024
Quantum Mechanics and Quantum Field Theory from Algebraic and Geometric Viewpoints (3/4)
De Albert Schwarz
On a problem of Whitney type in algebraic geometry
Apparaît dans la collection : Abel in Paris 2024
Whitney embedding theorem in differential geometry says that a small perturbation $f'$ of a map $f$ between two compact manifolds of dimensions $m$ and $n$ (hence $f'$ is isotopic, and a fortiori homotopic to $f$) is an embedding if $n^{2m}$ (the Whitney range). I will discuss a related question, asked by Borel and Haefliger, in complex algebraic geometry: can we write the cohomology class of an algebraic subvariety of a smooth projective variety as a combination with integral coefficients of classes of smooth subvarieties? Claire Voisin will discuss classical and recent results on this question, with emphasis on the Whitney range, which has recently been solved in the affirmative by Kollár and herself.
