Birational rigidity of complete intersections
Algebraic Geometry
2016-06-23 v2
Abstract
We prove that every smooth complete intersection X defined by s hypersurfaces of degree d_1, ... , d_s in a projective space of dimension d_1 + ... + d_s is birationally superrigid if 5s +1 is at most 2(d_1 + ... + d_s + 1)/sqrt{d_1...d_s}. In particular, X is non-rational and Bir(X)=Aut(X). We also prove birational superrigidity of singular complete intersections with similar numerical condition. These extend the results proved by Tommaso de Fernex.
Cite
@article{arxiv.1507.00285,
title = {Birational rigidity of complete intersections},
author = {Fumiaki Suzuki},
journal= {arXiv preprint arXiv:1507.00285},
year = {2016}
}
Comments
To appear in Mathematische Zeitschrift