Duke Mathematical Journal

Naïve noncommutative blowing up

D. S. Keeler, D. Rogalski, and J. T. Stafford

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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 cX 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.

Article information

Duke Math. J. Volume 126, Number 3 (2005), 491-546.

First available in Project Euclid: 11 February 2005

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Zentralblatt MATH identifier

Primary: 14A22: Noncommutative algebraic geometry [See also 16S38] 16P40: Noetherian rings and modules 16W50: Graded rings and modules
Secondary: 16S38: Rings arising from non-commutative algebraic geometry [See also 14A22] 18E15: Grothendieck categories


Keeler, D. S.; Rogalski, D.; Stafford, J. T. Naïve noncommutative blowing up. Duke Math. J. 126 (2005), no. 3, 491--546. doi:10.1215/S0012-7094-04-12633-8. http://projecteuclid.org/euclid.dmj/1108155760.

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