On the topology of projective subspaces in complex Fermat varieties

Alex Degtyarev; Ichiro Shimada

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On the topology of projective subspaces in complex Fermat varieties

机译：复杂费马品种中射影子空间的拓扑

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摘要

Let X be the complex Fermat variety of dimension n = 2d and degree m ＞ 2. We investigate the submodule of the middle homology group of X with integer coefficients generated by the classes of standard d-dimensional subspaces contained in X, and give an algebraic (or rather combinatorial) criterion for the primitivity of this submodule.

机译：令X为维n = 2d且度m＞ 2的复费马变种。我们研究X的中间同源群的子模块，该整数具有由X中包含的标准d维子空间类生成的整数系数，并给出代数（或更确切地说是组合的）准则来确定此子模块的原始性。

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来源
《Journal of the Mathematical Society of Japan》 |2016年第3期|975-996|共22页
作者
Alex Degtyarev; Ichiro Shimada;
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作者单位

Bilkent University Department of Mathematics 06800 Ankara, Turkey;

Department of Mathematics Graduate School of Science Hiroshima University 1-3-1 Kagamiyama Higashi-Hiroshima 739-8526, Japan;

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收录信息美国《科学引文索引》(SCI);
原文格式 PDF
正文语种 eng
中图分类
关键词
complex Fermat variety; middle homology group; Pham polyhedron;

机译：复杂的费马品种;中同源组潘多面体;

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1. Appendix to "Secant varieties and successive minima" by C. Soule: On linear subspaces contained in the secant varieties of a projective curve [J] . Claire Voisin Journal of algebraic geometry . 2004,第2期

机译：C. Soule的“正割变种和连续极小值”的附录：关于投影曲线的割割变种所包含的线性子空间
2. Appendix to "Secant varieties and successive minima" by C. Soule: On linear subspaces contained in the secant varieties of a projective curve [J] . Claire Voisin Journal of algebraic geometry . 2004,第2期

机译：C. Soule的“正割变种和连续极小值”的附录：关于投影曲线的割割变种所包含的线性子空间
3. AN EFFECTIVE SCHMIDT'S SUBSPACE THEOREM FOR HYPERSURFACES IN SUBGENERAL POSITION IN PROJECTIVE VARIETIES OVER FUNCTION FIELDS [J] . Le Giang Kodai Mathematical Journal . 2018,第1期

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机译：调查任务复杂性和成果品种对众包中的用户性能的影响
5. The values of the Milnor genus on smooth irreducible projective varieties over the complex numbers [D] . Johnston, Bryan Taylor 2000

机译：复数上光滑不可约投影品种上的Milnor属的值
6. Theorems of Barth-Lefschetz type for complex subspaces of homogeneous complex manifolds [O] . Andrew John Sommese 1977

机译：齐次复杂流形的复杂子空间的Barth-Lefschetz型定理
7. On the topology of projective subspaces in complex Fermat varieties [O] . Alex Degtyarev, Ichiro Shimada 2016

机译：关于复数费马品种投影子空间的拓扑
8. Secant Varieties and Successive Minima. Appendix: On Linear Subspaces Contained in the Secant Varieties of a Projective Curve. [R] . Soule, C., Voisin, C. 2001

机译：正确的品种和连续的极小。附录：关于投影曲线的正割变量中包含的线性子空间。

On the topology of projective subspaces in complex Fermat varieties

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