Stable rationality of orbifold Fano threefold hypersurfaces
Algebraic Geometry
2017-09-25 v3
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.
Keywords
Cite
@article{arxiv.1608.01186,
title = {Stable rationality of orbifold Fano threefold hypersurfaces},
author = {Takuzo Okada},
journal= {arXiv preprint arXiv:1608.01186},
year = {2017}
}
Comments
32 pages. Several mistakes are fixed. References updated