The pseudoautomorphism group of $\mathbb{P}^3$ blown-up at $8$ very general points

Abstract

We prove that the pseudoautomorphism group of a blow-up of $\mathbb{P}^3$ at $8$ very general points is trivial. We also establish the injectivity of the Coble representation associated to blow-ups of $\mathbb{P}^3$ at $r\ge 8$ general points, answering a question of Dolgachev--Ortland.