Geodesic
Stable rationality of higher dimensional conic bundles
Épijournal de Géométrie Algébrique, Tome 2 (2018)

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We prove that a very general nonsingular conic bundle $X\rightarrow\mathbb{P}^{n-1}$ embedded in a projective vector bundle of rank $3$ over $\mathbb{P}^{n-1}$ is not stably rational if the anti-canonical divisor of $X$ is not ample and $n\geq 3$. 
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     author = {Abban, Hamid and Okada, Takuzo},
     title = {Stable rationality of higher dimensional conic bundles},
     journal = {\'Epijournal de G\'eom\'etrie Alg\'ebrique},
     publisher = {mathdoc},
     volume = {2},
     year = {2018},
     doi = {10.46298/epiga.2018.volume2.4266},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.46298/epiga.2018.volume2.4266/}
}
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Abban, Hamid; Okada, Takuzo. Stable rationality of higher dimensional conic bundles. Épijournal de Géométrie Algébrique, Tome 2 (2018). doi: 10.46298/epiga.2018.volume2.4266

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