Naïve noncommutative blowing up

Abstract

Let B(X,$\mathscr{L}$,σ) be the twisted homogeneous coordinate ring of an irreducible variety X over an algebraically closed field k with dim X ≥ 2. Assume that c ∈ X and σ ∈ Aut(X) are in sufficiently general position. We show that if one follows the commutative prescription for blowing up X at c, but in this noncommutative setting, one obtains a noncommutative ring R = R(X,c,$\mathscr{L}$,σ) with surprising properties.