## Osaka Journal of Mathematics

### Trilinear forms and Chern classes of Calabi--Yau threefolds

#### Abstract

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

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

Dates
First available in Project Euclid: 8 April 2014

https://projecteuclid.org/euclid.ojm/1396966232

Mathematical Reviews number (MathSciNet)
MR3192539

Zentralblatt MATH identifier
1299.14035

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

#### Citation

Kanazawa, Atsushi; Wilson, P.M.H. Trilinear forms and Chern classes of Calabi--Yau threefolds. Osaka J. Math. 51 (2014), no. 1, 203--215.https://projecteuclid.org/euclid.ojm/1396966232

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