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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Families of rational surfaces preserving a cusp singularity

Author: Lee J. McEwan
Journal: Trans. Amer. Math. Soc. 321 (1990), 691-716
MSC: Primary 14J17; Secondary 14D20, 14J26
MathSciNet review: 968419
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Abstract: Families of rational surfaces containing resolutions of cusp singularities are explicitly constructed. It is proved that the families constructed are universal deformations at each point. Two different monodromy formulas are established; one of these is shown to be connected to automorphisms of Inoue-Hirzebruch surfaces. Some evidence (but no proof) is offered for the conjecture that finite base changes of the families we construct are the versal-deformation spaces for singular Inoue-Hirzebruch surfaces.

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  • [1] R. Friedman, preprint.
  • [2] -, Thesis, Harvard University, 1981.
  • [3] R. Friedman and R. Miranda, Smoothing cusp singularities of small length, Math. Ann. 263 (1983), 185-212. MR 698002 (85c:14003)
  • [4] R. Friedman and H. Pinkham, Smoothing of cusp singularities via triangle singularities, Compositio Math. 53 (1984), 303-316. MR 768826 (85m:14052)
  • [5] F. Hirzebruch, Hilbert Modular surfaces, Enseign. Math. 19 (1973). MR 0389921 (52:10750)
  • [6] M. Inoue, New surfaces with no meromorphic functions II, Complex Analysis and Algebraic Geometry (W. L. Baily and T. Shioda, eds.), Cambridge University Press, London, 1977. MR 0442297 (56:683)
  • [7] H. Laufer, Taut two-dimensional singularities, Math. Ann. 205 (1973). MR 0333238 (48:11563)
  • [8] -, Deformations of resolutions of two-dimensional singularities, Proc. Rice Conference on Complex Analysis (1972).
  • [9] E. Looijenga, Rational surfaces with an anticanonical cycle, Ann. of Math. 114 (1981). MR 632841 (83j:14030)
  • [10] U. Persson, On degenerations of algebraic surfaces, Mem. Amer. Math. Soc. 11 (1977), 189. MR 0466149 (57:6030)
  • [11] H. Pinkham, Automorphisms of cusps and Inoue-Hirzebruch surfaces, Compositio Math. 52 (1984). MR 756724 (85m:32024)
  • [12] J. Wahl, Smoothing of normal surface singularities, Topology 20 (1981). MR 608599 (83h:14029)

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Article copyright: © Copyright 1990 American Mathematical Society

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