Birational rigidity of Fano varieties and field extensions

János Kollár

doi:10.1134/S008154380901012X

Birational rigidity of Fano varieties and field extensions

János Kollár

Mathematics

Research output: Contribution to journal › Article › peer-review

5 Scopus citations

Abstract

This note studies the behavior of birational rigidity and universal birational rigidity in extensions of algebraically closed fields.

Original language	English (US)
Pages (from-to)	96-101
Number of pages	6
Journal	Proceedings of the Steklov Institute of Mathematics
Volume	264
Issue number	1
DOIs	https://doi.org/10.1134/S008154380901012X
State	Published - Apr 2009

All Science Journal Classification (ASJC) codes

Mathematics (miscellaneous)

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10.1134/S008154380901012X

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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.",

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doi = "10.1134/S008154380901012X",

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N1 - 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.

PY - 2009/4

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N2 - This note studies the behavior of birational rigidity and universal birational rigidity in extensions of algebraically closed fields.

AB - This note studies the behavior of birational rigidity and universal birational rigidity in extensions of algebraically closed fields.

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JO - Proceedings of the Steklov Institute of Mathematics

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Birational rigidity of Fano varieties and field extensions

Abstract

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