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2013 Moduli spaces for point modules on naïve blowups
Thomas Nevins, Susan Sierra
Algebra Number Theory 7(4): 795-834 (2013). DOI: 10.2140/ant.2013.7.795


The naïve blowup algebras developed by Keeler, Rogalski, and Stafford, after examples of Rogalski, are the first known class of connected graded algebras that are noetherian but not strongly noetherian. This failure of the strong noetherian property is intimately related to the failure of the point modules over such algebras to behave well in families: puzzlingly, there is no fine moduli scheme for such modules although point modules correspond bijectively with the points of a projective variety X. We give a geometric structure to this bijection and prove that the variety X is a coarse moduli space for point modules. We also describe the natural moduli stack X for embedded point modules — an analog of a “Hilbert scheme of one point” — as an infinite blowup of X and establish good properties of X. The natural map XX is thus a kind of “Hilbert–Chow morphism of one point" for the naïve blowup algebra.


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Thomas Nevins. Susan Sierra. "Moduli spaces for point modules on naïve blowups." Algebra Number Theory 7 (4) 795 - 834, 2013.


Received: 28 October 2010; Revised: 6 April 2012; Accepted: 5 November 2012; Published: 2013
First available in Project Euclid: 20 December 2017

zbMATH: 1273.14010
MathSciNet: MR3095227
Digital Object Identifier: 10.2140/ant.2013.7.795

Primary: 16S38
Secondary: 14A20 , 14D22 , 16D70 , 16W50

Keywords: naïve blowup , point module , point space

Rights: Copyright © 2013 Mathematical Sciences Publishers

Vol.7 • No. 4 • 2013
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