Stable rationality of orbifold Fano 3-fold hypersurfaces

IF 0.9 1区数学 Q2 MATHEMATICS

Journal of Algebraic Geometry Pub Date : 2016-08-03 DOI:10.1090/JAG/712

Takuzo Okada

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引用次数: 13

Abstract

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

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轨道Fano三重超曲面的稳定合理性

完整地确定了非常一般的拟光滑Fano 3 - 3折加权超曲面的合理性，并确定了除三次3 - 3折外的其他超曲面的稳定合理性。更确切地说，我们证明了(i)指数11或22的非常一般的Fano 3-fold加权超曲面除了可能的三次3-fold外，是不稳定有理的;(ii)指数大于22的Fano 3-fold加权超曲面的2727个族中，有77个特定族的非常一般的成员是不稳定有理的，其余2020个族由有理变种组成。

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来源期刊

Journal of Algebraic Geometry 数学-数学

CiteScore

2.70

自引率

5.60%

发文量

审稿时长

>12 weeks

期刊介绍： The Journal of Algebraic Geometry is devoted to research articles in algebraic geometry, singularity theory, and related subjects such as number theory, commutative algebra, projective geometry, complex geometry, and geometric topology. This journal, published quarterly with articles electronically published individually before appearing in an issue, is distributed by the American Mathematical Society (AMS). In order to take advantage of some features offered for this journal, users will occasionally be linked to pages on the AMS website.