Stable Rationality of Cyclic Covers of Projective Spaces
Stable Rationality of Cyclic Covers of Projective Spaces
复制标题
射影空间循环覆盖的稳定有理性
DOI：
10.1017/s0013091518000755
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发表时间：
2019
影响因子：
0.7
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
本文的主要目的是证明当n ≥ 3且d ≥ n + 1时，沿着一个非常一般的d次因子分支的n阶循环覆盖不是稳定有理的.这推广了Colliot-Thélène和Pirutka的结果。还讨论了完全相交上的循环覆盖的推广及其在合适的Fano流形上的应用。
The main aim of this paper is to show that a cyclic cover of ℙn branched along a very general divisor of degree d is not stably rational, provided that n ≥ 3 and d ≥ n + 1. This generalizes the result of Colliot-Thélène and Pirutka. Generalizations for cyclic covers over complete intersections and applications to suitable Fano manifolds are also discussed.