@article{66f6edd295804348a08ec914a8640022,
title = "Birational rigidity of Fano varieties and field extensions",
abstract = "This note studies the behavior of birational rigidity and universal birational rigidity in extensions of algebraically closed fields.",
author = "J{\'a}nos Koll{\'a}r",
note = "Funding Information: Note that τ does not extract any divisor; thus τ/G does not extract any divisor either. Since XU′ has relative Picard number 1 over U, we conclude that τ/G does not contract any divisor either. By a lemma of Matsusaka and Mumford (cf. [9, 5.6]), this implies that τ/G is an isomorphism. □ ACKNOWLEDGMENTS I thank I. Cheltsov for useful e-mails and comments. Partial financial support was provided by the NSF, project no. DMS-0500198.",
year = "2009",
month = apr,
doi = "10.1134/S008154380901012X",
language = "English (US)",
volume = "264",
pages = "96--101",
journal = "Proceedings of the Steklov Institute of Mathematics",
issn = "0081-5438",
publisher = "Pleiades Publishing",
number = "1",
}