Birational Invariants and Decomposition of the Diagonal

Chapter
Part of the Lecture Notes of the Unione Matematica Italiana book series (UMILN, volume 26)

Abstract

We give a rather detailed account of cohomological and Chow-theoretic methods in the study of the stable version of the Lroth problem, which ask how to distinguish (stably) rational varieties from general unirational varieties. In particular, we study the notion of Chow or cohomological decomposition of the diagonal, which is a necessary criterion for stable rationality. Having better stability properties than the previously known obstructions under specialization with mildly singular central fibers, it has been very useful in the recent study of rationality questions.

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