Stable rationality of orbifold Fano 3-fold hypersurfaces
Stable rationality of orbifold Fano 3-fold hypersurfaces
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Orbifold Fano 3 重超曲面的稳定合理性
DOI：
10.1090/jag/712
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发表时间：
2019
影响因子：
1.8
通讯作者：
Takuzo Okada
中科院分区：
文献类型：
--
作者：
Bhargav Bhatt;Karl Schwede and Shunsuke Takagi;小池寿俊・大城紀代市;高木 俊輔;GangYong Lee ・大城紀代市;Mitsuyasu Hashimoto;高木 俊輔;橋本光靖;小池寿俊;Shunsuke Takagi;鈴木裕也・山浦浩太;Mitsuyasu Hashimoto;Shunsuke Takagi;橋本光靖;小池寿俊;大城紀代市;Shunsuke Takagi;橋本光靖;上村英男・菊政勲・倉富要輔;Shunsuke Takagi;大城紀代市;Shunsuke Takagi;Takuzo Okada;小池寿俊;Shunsuke Takagi;Takuzo Okada
我们完全确定了非常一般的拟光滑Fano 3重加权超曲面的合理性，并确定了除三次3重加权超曲面以外的拟光滑Fano 3重加权超曲面的稳定合理性。更精确地，我们证明了：（i）除了可能的三次Fano三重加权超曲面之外，指数为1或2的非常一般的Fano三重加权超曲面都不是稳定有理的;（ii）在指数大于2的27个Fano三重加权超曲面族中，有7个族中的非常一般的成员不是稳定有理的，其余20个族都是有理簇.
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.