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The technology of noncommutative blowups Rogalski, Daniel


Van den Bergh defined a notion of blowing up a noncommutative surface at a point lying on a commutative divisor in the surface. The definition is made by constructing a Rees ring in a certain category of functors with adjoints. We show how to make the adjoint functors more explicit using what is known as projective effacements. This allows us to define blowups more generally, and also helps to make it clear that the coordinate rings of Van den Bergh's blowups of the Sklyanin projective plane are the same as the ring-theoretic blowups studied by Sierra, Stafford, and the author.

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