Vol. 7, No. 4, 2013

Download this article
Download this article For screen
For printing
Recent Issues

Volume 10
Issue 9, 1845–2052
Issue 8, 1601–1843
Issue 7, 1373–1600
Issue 6, 1147–1371
Issue 5, 939–1146
Issue 4, 695–938
Issue 3, 451–694
Issue 2, 215–450
Issue 1, 1–214

Volume 9, 10 issues

Volume 8, 10 issues

Volume 7, 10 issues

Volume 6, 8 issues

Volume 5, 8 issues

Volume 4, 8 issues

Volume 3, 8 issues

Volume 2, 8 issues

Volume 1, 4 issues

The Journal
Cover
Editorial Board
Editors' Addresses
Editors' Interests
About the Journal
Scientific Advantages
Submission Guidelines
Submission Form
Subscriptions
Editorial Login
Contacts
Author Index
To Appear
 
ISSN: 1944-7833 (e-only)
ISSN: 1937-0652 (print)
Moduli spaces for point modules on naïve blowups

Thomas A. Nevins and Susan J. Sierra

Vol. 7 (2013), No. 4, 795–834
Abstract

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 X X is thus a kind of “Hilbert–Chow morphism of one point" for the naïve blowup algebra.

Keywords
naïve blowup, point module, point space
Mathematical Subject Classification 2010
Primary: 16S38
Secondary: 16D70, 16W50, 14A20, 14D22
Milestones
Received: 28 October 2010
Revised: 6 April 2012
Accepted: 5 November 2012
Published: 29 August 2013
Authors
Thomas A. Nevins
Department of Mathematics
University of Illinois at Urbana–Champaign
1409 West Green Street
MC-382
Urbana, IL
61801
United States
Susan J. Sierra
School of Mathematics
The University of Edinburgh
James Clerk Maxwell Building
The King’s Buildings
Mayfield Road
Edinburgh
EH9 3JZ
United Kingdom
http://www.maths.ed.ac.uk/~ssierra/