Birationally rigid Fano-Mori fibre spaces
Forum of Mathematics, Sigma, Tome 12 (2024)
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In this paper, we prove the birational rigidity of Fano-Mori fibre spaces $\pi \colon V\to S$, every fibre of which is a Fano complete intersection of index 1 and codimension $k\geqslant 3$ in the projective space ${\mathbb P}^{M+k}$ for M sufficiently high, satisfying certain natural conditions of general position, in the assumption that the fibre space $V/S$ is sufficiently twisted over the base. The dimension of the base S is bounded from above by a constant, depending only on the dimension M of the fibre (as the dimension of the fibre M grows, this constant grows as $\frac 12 M^2$).
@article{10_1017_fms_2024_84,
author = {Aleksandr Pukhlikov},
title = {Birationally rigid {Fano-Mori} fibre spaces},
journal = {Forum of Mathematics, Sigma},
publisher = {mathdoc},
volume = {12},
year = {2024},
doi = {10.1017/fms.2024.84},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1017/fms.2024.84/}
}
Aleksandr Pukhlikov. Birationally rigid Fano-Mori fibre spaces. Forum of Mathematics, Sigma, Tome 12 (2024). doi: 10.1017/fms.2024.84
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