In this survey paper birational geometry of higher-dimensional rationally connected varieties is discussed. In higher dimensions the classical rationality problem generalizes to the problem of description of the structures of a rationally connected fiber space on a given variety. We discuss the key concept of birational rigidity and present examples of Fano fiber spaces with finitely many rationally connected structures.
CITATION STYLE
Pukhlikov, A. V. (2010). The rationality problem and birational rigidity. In Progress in Mathematics (Vol. 282, pp. 275–311). Springer Basel. https://doi.org/10.1007/978-0-8176-4934-0_11
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