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$K3$ surfaces in $\mathbb P^1 \times \mathbb P^1 \times \mathbb P^1$

I am considering $K3$ surfaces in $\mathbb P^1 \times \mathbb P^1 \times \mathbb P^1$ with an automorphism that preserves an ample divisor class. For an automorphism $\rho$ of a $K3$ surface, let ${\...
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