关于 Calabi-Yau 超曲面的 level
代数几何
2018-02-15 v2 交换代数
摘要
Boix-De Stefani-Vanzo 借助此前由 \`Alvarez-Montaner-Blickle-Lyubeznik 考虑的理想的链的稳定化，定义了有限域上光滑射影超曲面的 level 这一概念，并证明了在椭圆曲线情形下 level 为 1 当且仅当其为寻常的，否则为 2。在此我们将他们的定理推广到 Calabi-Yau 超曲面的情形，将其 level 与 Blickle-Musta\c{t}\u{a}-Smith 的 -跳跃指数以及 Musta\c{t}\u{a}-Zhang 的 Hartshorne-Speiser-Lyubeznik 数相联系。
引用
@article{arxiv.1801.04893,
title = {On the level of a Calabi-Yau hypersurface},
author = {Stiofáin Fordham},
journal= {arXiv preprint arXiv:1801.04893},
year = {2018}
}
备注
7 pages. This version: (old) proposition 7 missing an hypothesis and proof was incorrect, but it actually follows for CYs from the proof of (old) proposition 17 so an explicit F-splitting is unnecessary; the paper is consequently reorganised. Some other relatively minor errata/notation corrected. Main result is unaffected. Thanks to Adrian Langer for a number of useful comments