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Transactions of the American Mathematical Society

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Clifford indices of ribbons

Authors: David Eisenbud and Mark Green
Journal: Trans. Amer. Math. Soc. 347 (1995), 757-765
MSC: Primary 14H45; Secondary 14C20
MathSciNet review: 1273474
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Abstract: We present a theory of "limit linear series" for rational ribbons-- that is, for schemes that are double structures on $ {P^1}$. This allows us to define a "linear series Clifford index" for ribbons. Our main theorem shows that this is the same as the Clifford index of ribbons studied by Eisenbud-Bayer in this same volume. This allows us to prove that the Clifford index is semicontinuous in degenerations from a smooth curve to a ribbon. A result of Fong [1993] then shows that ribbons may be deformed to smooth curves of the same Clifford index. Thus the Canonical Curve Conjecture of Green [1984] would follow, at least for a general smooth curve of each Clifford index, from the corresponding statement for ribbons.

References [Enhancements On Off] (What's this?)

  • [D] Bayer and D. Eisenbud, Ribbons and their canonical embeddings, Trans. Amer. Math. Soc. 347 (1995), 719-756. MR 1273472 (95g:14032)
  • [C] D'Souza, Compactiftcation of generalized Jacobians, Proc. Indian Acad. Sci. Math. Sci. 88 (1979), 419-457. MR 569548 (81h:14004)
  • [D] Eisenbud, Green's Conjecture: an orientation for algebraists, Free Resolutions in Commutative Algebra and Algebraic Geometry, Sundance 90, (D. Eisenbud and C. Huneke, eds.), Jones and Bartlett, 1992. MR 1165318 (93e:13020)
  • [L] -Y. Fong, Rational ribbons and deformations of hyperelliptic curves, J. Algebraic Geom. 2 (1993), 295-307. MR 1203687 (94c:14020)
  • [M] Green, Koszul cohomology and the geometry of projective varieties, (with an appendix by M. Green and R. Lazarsfeld), J. Differential Geom. 19 (1984), 125-171. MR 739785 (85e:14022)
  • 1. Jürgen Herzog, Canonical Koszul cycles, Aportationes Mat. 6 (1992), 33-41. MR 1310371 (95k:13018)

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