New canonical triple covers of surfaces

We construct a surface of general type with canonical map of degree 12 which factors as a triple cover and a bidouble cover of $\mathbb P^2$. We also show the existence of a smooth surface with $q=0,$ $χ=13$ and $K^2=9χ$ such that its canonical map is either of degree 3 onto a surface of general type or of degree 9 onto a rational surface.

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