Abstract / Description of output
The birational superrigidity and, in particular, the non-rationality of a smooth three-dimensional quartic was proved by V. Iskovskikh and Yu. Manin in 1971, and this led immediately to a counterexample to the three-dimensional Lüroth problem. Since then, birational rigidity and superrigidity have been proved for a broad class of higher-dimensional varieties, among which the Fano varieties occupy the central place. The present paper is a survey of the theory of birationally rigid Fano varieties.
| Original language | English |
|---|---|
| Pages (from-to) | 875-965 |
| Number of pages | 91 |
| Journal | Russian Mathematical Surveys |
| Volume | 60 |
| Issue number | 5 |
| DOIs | |
| Publication status | Published - 31 Oct 2005 |