For every projective variety of dimension at least two that is not a rational surface, blowing up sufficiently many very general points yields a variety with no nontrivial automorphism.
Special rays in the Mori cone of a projective variety
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Automorphisms of very general blow up
For every projective variety of dimension at least two that is not a rational surface, blowing up sufficiently many very general points yields a variety with no nontrivial automorphism.