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arXiv · 1608.01186

Stable rationality of orbifold Fano threefold hypersurfaces

Takuzo Okada
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Abstract

We determine the rationality of very general quasismooth Fano 3-fold weighted hypersurfaces completely and determine the stable rationality of them except for cubic 3-folds. More precisely we prove that (i) very general Fano 3-fold weighted hypersurfaces of index 1 or 2 are not stably rational except possibly for the cubic threefolds, (ii) among the 27 families of Fano 3-fold weighted hypersurfaces of index greater than 2, very general members of specific 7 families are not stably rational and the remaining 20 families consists of rational varieties.

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Takuzo Okada. 2016-08-03. Stable rationality of orbifold Fano threefold hypersurfaces. https://arxiv.org/abs/1608.01186

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