Journal of the Mathematical Society of Japan

On the topology of projective subspaces in complex Fermat varieties


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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.

Article information

J. Math. Soc. Japan Volume 68, Number 3 (2016), 975-996.

First available in Project Euclid: 19 July 2016

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 14F25: Classical real and complex (co)homology
Secondary: 14J70: Hypersurfaces

complex Fermat variety middle homology group Pham polyhedron


DEGTYAREV, Alex; SHIMADA, Ichiro. On the topology of projective subspaces in complex Fermat varieties. J. Math. Soc. Japan 68 (2016), no. 3, 975--996. doi:10.2969/jmsj/06830975.

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