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Transactions of the American Mathematical Society

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



Curves on normal surfaces

Author: Gunnar Fløystad
Journal: Trans. Amer. Math. Soc. 352 (2000), 5485-5510
MSC (2000): Primary 14H50
Published electronically: August 8, 2000
MathSciNet review: 1443874
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Abstract: We study locally Cohen-Macaulay space curves lying on normal surfaces. We prove some theorems on the behaviour of the cohomology functions and initial ideals of such space curves, which give a basic distinction between those curves and curves lying on non-normal surfaces.

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  • [Ba-Fo] C. Banica, O. Forster. Multiplicity structures on space curves. Lefschetz Centennial Conf., Part I, Contemp. Math. 58, (1986), 47-64. MR 88c:32018
  • [Ba-St] D. Bayer, M. Stillman. A criterion for detecting m-regularity. Inventiones Mathematicae 87 (1987), 1-11. MR 87k:13019
  • [Co] M. Cook. The connectedness of space curve invariants. Compositio Mathematica 111 (1998), 221-244. MR 99a:14040
  • [Ei] D. Eisenbud. Commutative algebra with a view towards algebraic geometry. GTM 150, Springer Verlag (1995). MR 97a:13001
  • [Fl] G. Fløystad. Higher initial ideals of homogeneous ideals. Memoirs of the American Mathematical Society 134 (1998), no. 638. MR 98m:13021
  • [Fl-Gr] G. Fløystad, M. Green. The information encoded in initial ideals. To appear in Transactions of the American Mathematical Society.
  • [Gi] S. Giuffrida. Graded Betti numbers and Rao module of a curve lying on a smooth cubic surface in $\mathbf{P}^3$. Queen's Papers in Pure and Appl. Math., 88 (1991), A1-A61. MR 93g:14035
  • [Ha] R. Hartshorne. Generalized divisors on Gorenstein schemes. K-theory 8 (1994), 287-339. MR 95k:14008
  • [Li] R. Liebling. Classification of space curves using initial ideals. Ph.D. thesis, University of California at Berkeley (1996).
  • [MD-Pe] M. Martin-Deschamps, D. Perrin. Sur la classification des courbes gauches. Astérisque 184-185 (1990). MR 91h:14039

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Additional Information

Gunnar Fløystad
Affiliation: Matematisk Institutt, Johs. Brunsgt. 12, 5008 Bergen, Norway

Keywords: Space curves, normal surfaces, initial ideals
Received by editor(s): July 4, 1996
Received by editor(s) in revised form: September 22, 1997
Published electronically: August 8, 2000
Article copyright: © Copyright 2000 American Mathematical Society