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A Note About Linear Systems on Curves

Published online by Cambridge University Press:  20 November 2018

Allen Tannenbaum
Allen Tannenbaum*
Affiliation:
Center for Mathematical System Theory, Department of Mathematics, University of Florida, Gainesville, Florida 32611, U.S.A.
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Abstract

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Inverting the Castelnuovo bound in two ways, we show that for given integers p ≥ 0, d > 1, n > 1, we can find a smooth irreducible curve of genus p which contains a linear system of degree d and of maximal dimension relative to the given data p and d, and a smooth irreducible curve of genus p which contains a linear system of dimension n and of minimal degree relative to the data p and n.

Keywords

14H4514C20
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 27 , Issue 3 , 01 September 1984 , pp. 371 - 374
Copyright
Copyright © Canadian Mathematical Society 1984

References

1. Griffiths, P. and Harris, J.. Principles of Algebraic Geometry. John Wiley and Sons, New York (1978).Google Scholar
2. Tannenbaum, A.. Families of algebraic curves with nodes. Compositio Math. 41 (1980), 107–126.Google Scholar