Birationally rigid Fano hypersurfaces
By A. Pukhlikov. 2002
86 citations recorded by the source corpus.
We prove that a smooth Fano hypersurface $V=V_M\subset{\Bbb P}^M$, $M\geq 6$, is birationally superrigid. In particular, it cannot be fibered into uniruled varieties by a non-trivial rational map and each birational map onto a minimal Fano variety of the same dimension is a biregular isomorphism. The proof is based on the method of maximal singularities combined with the connectedness principle of Shokurov and Koll\' ar.
Subfields: Applied Mathematics, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/35dac30e302791c2b61a9482ca02214a4f78ef1f
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In Applied Mathematics
- L. Ein
- Tommaso de Fernex
- J.-J. Sansuc
- J.-L. Colliot-Th'elene
- M. Mustaţă
- Chi Li
- Mattias Jonsson
- S. Boucksom
In Geometry and Topology
- M. Mustaţă
- Tommaso de Fernex
- L. Ein
- J.-J. Sansuc
- J.-L. Colliot-Th'elene
- Chi Li
- H. Blum
- Mattias Jonsson
Citations in the corpus
- Birationally rigid hypersurfaces (2006, result): “2]); the same result is also claimed in [Pu5], but the given proof only applies to general hypersurfaces.”
- The rationality problem for fields of invariants under linear algebraic groups (with special regards to the Brauer group) (2005, background): “It has witnessed a strong development: birational rigidity and birational super-rigidity, work of Iskovskikh [56], Pukhlikov [112,113], de Fernex-Ein-Mustaţă [38].”
- Multiplicities and log canonical threshold (2002, methodology): “ (1). In this spirit, we apply Theorem 0.1 in [DEM] to give an upper bound for the log canonical threshold of a generic projection of a projective variety. This improves a bound due to Pukhlikov from [Pu1], bound which plays a major role in his proof of the fact that a smooth hypersurface of degree ”