Osaka Journal of Mathematics

Trilinear forms and Chern classes of Calabi--Yau threefolds

Atsushi Kanazawa and P.M.H. Wilson

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Let $X$ be a Calabi--Yau threefold and $\mu$ the symmetric trilinear form on the second cohomology group $H^{2}(X,\mathbb{Z})$ defined by the cup product. We investigate the interplay between the Chern classes $c_{2}(X)$, $c_{3}(X)$ and the trilinear form $\mu$, and demonstrate some numerical relations between them. When the cubic form $\mu(x,x,x)$ has a linear factor over $\mathbb{R}$, some properties of the linear form and the residual quadratic form are also obtained.

Article information

Osaka J. Math. Volume 51, Number 1 (2014), 203-215.

First available in Project Euclid: 8 April 2014

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 14J32: Calabi-Yau manifolds 14F45: Topological properties


Kanazawa, Atsushi; Wilson, P.M.H. Trilinear forms and Chern classes of Calabi--Yau threefolds. Osaka J. Math. 51 (2014), no. 1, 203--215.

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