Universal Chow group of 0-cycles and stable rationality
Apparaît également dans la collection : Algèbre, Géométrie et Physique : une conférence en l'honneur
Much work has been done in the 70's to solve the Lüroth problem of distinguishing unirational from rational (or stably rational) varieties. For 3-dimensional unirational varieties, the only stable birational invariant used up to now has been the Artin-Mumford invariant.We showusing the universal Chow group of zero-cycles that some unirational threefolds with trivial Artin-Mumford invariant are not stably rational.Some of these examples have the following property: they do not admit a universal codimension 2 cycle,which prevents their stable rationality and exhibits a new phenomenon in the theory of algebraic cycles.
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