Surveys in Differential Geometry

Volume 21 (2016)

Stable birational invariants and the Lüroth problem

Pages: 313 – 342



Claire Voisin (CNRS, Institut de Mathématiques de Jussieu, Paris, France)


We describe recent progress on rationality and stable rationality questions. We discuss the cohomological or Chow decomposition of the diagonal, a very strong stably birationally invariant property which controls many of the previously defined stable birational invariants. On the other hand, it behaves very well under specialization and desingularization of mild singularities.

Published 13 January 2022