A compactification of open varieties
HTML articles powered by AMS MathViewer
- by Yi Hu PDF
- Trans. Amer. Math. Soc. 355 (2003), 4737-4753 Request permission
Abstract:
In this paper we prove a general method to compactify certain open varieties by adding normal crossing divisors. This is done by showing that blowing up along an arrangement of subvarieties can be carried out. Important examples such as Ulyanov’s configuration spaces and complements of arrangements of linear subspaces in projective spaces, etc., are covered. Intersection ring and (nonrecursive) Hodge polynomials are computed. Furthermore, some general structures arising from the blowup process are also described and studied.References
- William Fulton and Robert MacPherson, A compactification of configuration spaces, Ann. of Math. (2) 139 (1994), no. 1, 183–225. MR 1259368, DOI 10.2307/2946631
- Yi Hu, Relative geometric invariant theory and universal moduli spaces, Internat. J. Math. 7 (1996), no. 2, 151–181. MR 1382720, DOI 10.1142/S0129167X96000098
- Yi Hu, Moduli spaces of stable polygons and symplectic structures on $\overline {\scr M}{}_{0,n}$, Compositio Math. 118 (1999), no. 2, 159–187. MR 1713309, DOI 10.1023/A:1001055409867
- Sean Keel, Intersection theory of moduli space of stable $n$-pointed curves of genus zero, Trans. Amer. Math. Soc. 330 (1992), no. 2, 545–574. MR 1034665, DOI 10.1090/S0002-9947-1992-1034665-0
- Frances Clare Kirwan, Partial desingularisations of quotients of nonsingular varieties and their Betti numbers, Ann. of Math. (2) 122 (1985), no. 1, 41–85. MR 799252, DOI 10.2307/1971369
- R. MacPherson and C. Procesi, Making conical compactifications wonderful, Selecta Math. (N.S.) 4 (1998), no. 1, 125–139. MR 1623714, DOI 10.1007/s000290050027
- Alexander P. Ulyanov, Polydiagonal compactification of configuration spaces, J. Algebraic Geom. 11 (2002), no. 1, 129–159. MR 1865916, DOI 10.1090/S1056-3911-01-00293-4
Additional Information
- Yi Hu
- Affiliation: Department of Mathematics, University of Arizona, Tucson, Arizona 85721
- Email: yhu@math.arizona.edu
- Received by editor(s): November 14, 2000
- Published electronically: July 24, 2003
- © Copyright 2003 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 355 (2003), 4737-4753
- MSC (2000): Primary 14C05; Secondary 05C30, 14N20
- DOI: https://doi.org/10.1090/S0002-9947-03-03247-1
- MathSciNet review: 1997581