AHMADINEZHAD, H. and OKADA, T., 2018. Stable rationality of higher dimensional conic bundles. Epijournal de Geometrie Algebrique, 2:5.
We prove that a very general nonsingular conic bundle X → Pn−1 embedded in a projective vector bundle of rank 3 over P
n−1 is not stably rational if the anti-canonical divisor of X is not ample
and n ≥ 3.
This is an Open Access Article. It is published by Episciences under the Creative Commons Attribution-ShareAlike 4.0 International (CC BY-SA 4.0) licence. Full details of this licence are available at: http://creativecommons.org/licenses/by-sa/4.0/