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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

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.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1995-1273474-7
PII: S 0002-9947(1995)1273474-7
Article copyright: © Copyright 1995 American Mathematical Society