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The genus of curves on the three dimensional quadric

Published online by Cambridge University Press:  22 January 2016

Mark Andrea A. De Cataldo
Mark Andrea A. De Cataldo*
Affiliation:
Department of Mathematics, Washington University in St. Louis Campus, Box 1146 Saint Louis 63130 (MO), U. S. A.mde@math.wustl.edu
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Abstract

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By means of an ad hoc modification of the so-called “Castelnuovo-Harris analysis” we derive an upper bound for the genus of integral curves on the three dimensional nonsingular quadric which lie on an integral surface of degree 2/c, as a function of k and the degree d of the curve. In order to obtain this we revisit the Uniform Position Principle to make its use computation-free. The curves which achieve this bound can be conveniently characterized.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 147 , September 1997 , pp. 193 - 211
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1997

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