Geodesic
Variation of stable birational types in positive characteristic
Épijournal de Géométrie Algébrique, Tome 3 (2019)

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Let k be an uncountable algebraically closed field and let Y be a smooth projective k-variety which does not admit a decomposition of the diagonal. We prove that Y is not stably birational to a very general hypersurface of any given degree and dimension. We use this to study the variation of the stable birational types of Fano hypersurfaces over fields of arbitrary characteristic. This had been initiated by Shinder, whose method works in characteristic zero. 
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     author = {Schreieder, Stefan},
     title = {Variation of stable birational types in positive characteristic},
     journal = {\'Epijournal de G\'eom\'etrie Alg\'ebrique},
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     volume = {3},
     year = {2019},
     doi = {10.46298/epiga.2020.volume3.5728},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.46298/epiga.2020.volume3.5728/}
}
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Schreieder, Stefan. Variation of stable birational types in positive characteristic. Épijournal de Géométrie Algébrique, Tome 3 (2019). doi: 10.46298/epiga.2020.volume3.5728

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