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Can you give an example of a Calabi-Yau six-fold?
I think that the most simple example is generated by the octic in \(CP^7\) with an Euler number 720608 . Do you agree?
If by 6-fold you mean of complex dimension 6, then it's correct. More generally, an hypersurface of degree $n+1$ in $CP^n$ is a Calabi-Yau of complex dimension $n-1$. Still more generally, complete intersections of degrees $(d_1,..., d_k)$ in $CP^n$ with $d_1+...+d_k=n+1$ are Calabi-Yau of complex dimensions $n-k$. For example, complete intersections of degrees $(2,7)$, $(3,6)$ or $(4,5)$ in $CP^8$ are Calabi-Yau of complex dimension $6$, with Euler numbers respectively $575876$, $325188$ and $185120$ (if I am not mistaken).
@40227, many thanks for your answer. You are very right, the Euler numbers that you are providing are correct. Now I will find examples with triple intersections. All the best.
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