scholarly journals The motivic nearby fiber and degeneration of stable rationality

2019 ◽  
Vol 217 (2) ◽  
pp. 377-413
Author(s):  
Johannes Nicaise ◽  
Evgeny Shinder
Keyword(s):  
Stable Rationality

Stable rationality of the group Spin10

2000 ◽  
Vol 55 (1) ◽  
pp. 178-179 ◽  
Author(s):  
Vsevolod E Kordonskii
Keyword(s):  
Stable Rationality

scholarly journals Stable rationality and conic bundles

2015 ◽  
Vol 365 (3-4) ◽  
pp. 1201-1217 ◽  
Author(s):  
Brendan Hassett ◽  
Andrew Kresch ◽  
Yuri Tschinkel
Keyword(s):  
Stable Rationality ◽  
Conic Bundles

scholarly journals Stable Rationality of del Pezzo Fibrations of Low Degree Over Projective Spaces

2018 ◽  
Vol 2020 (23) ◽  
pp. 9075-9119 ◽  
Author(s):  
Igor Krylov ◽  
Takuzo Okada
Keyword(s):  
Projective Space ◽  
Three Dimensional ◽  
Projective Spaces ◽  
Canonical Divisor ◽  
Stable Rationality ◽  
Higher Dimensional ◽  
Low Degree ◽  
Del Pezzo

Abstract The main aim of this article is to show that a very general three-dimensional del Pezzo fibration of degrees 1, 2, and 3 is not stably rational except for a del Pezzo fibration of degree 3 belonging to explicitly described two families. Higher-dimensional generalizations are also discussed and we prove that a very general del Pezzo fibration of degrees 1, 2, and 3 defined over the projective space is not stably rational provided that the anti-canonical divisor is not ample.

scholarly journals Stable rationality of certain invariant fields

2003 ◽  
Vol 269 (2) ◽  
pp. 373-380 ◽  
Author(s):  
Esther Beneish
Keyword(s):  
Stable Rationality

scholarly journals ON THE RATIONALITY OF ALMOST SIMPLE ALGEBRAIC GROUPS

1999 ◽  
Vol 10 (05) ◽  
pp. 643-665
Author(s):  
NGUYÊÑ QUÔĆ THǍŃG
Keyword(s):  
Dynkin Diagram ◽  
Algebraic Groups ◽  
Simple Groups ◽  
Connected Components ◽  
Weak Approximation ◽  
Stable Rationality ◽  
Almost Simple Groups ◽  
Anisotropic Kernel

We prove the stable rationality of almost simple adjoint algebraic groups, the connected components of the Dynkin diagram of anisotropic kernel of which contain at most two vertices. The (stable) rationality of many isotropic almost simple groups with small anisotropic kernel and some related results in weak approximation over arbitrary fields are discussed.

Stable rationality of certain PGLn-quotients

1991 ◽  
Vol 104 (1) ◽  
pp. 179-199 ◽  
Author(s):  
Christine Bessenrodt ◽  
Lieven Le Bruyn
Keyword(s):  
Stable Rationality

scholarly journals On stable rationality of Fano threefolds and del Pezzo fibrations

2019 ◽  
Vol 2019 (751) ◽  
pp. 275-287 ◽  
Author(s):  
Brendan Hassett ◽  
Yuri Tschinkel
Keyword(s):  
Fano Threefolds ◽  
Stable Rationality ◽  
Del Pezzo

AbstractWe prove that very general non-rational Fano threefolds which are not birational to cubic threefolds are not stably rational.

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