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Description:
We study the Mukai system $M rightarrow mathbb{P}^5$ of rank two and genus two from three different points of view. We compute the degrees and multiplicities of the irreducible components of the fibers over non-reduced curves. We provide examples of algebraically coisotropic and constant cycle subvarieties in $M$. We find all smooth birational models of $M$ in a sequence of flops.