Stable rationality of orbifold Fano threefold hypersurfaces

2016/08/03 by Okada, Takuzo · 4 citations
#Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1608.01186

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.

Cited by

• A survey on birational Rigidity of threefold Weighted Complete Intersections
• Automorphism groups and cylindricity of weighted hypersurface Fano threefolds
• Nonrational varieties with unirational parametrizations of coprime degrees
• Weighted four-dimensional Fano hypersurfaces of K3 type

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• Smooth weighted hypersurfaces that are not stably rational
• On stable rationality of Fano threefolds and del Pezzo fibrations
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• K-stablity of Fano threefold hypersurfaces of index 1