The genus of curves on the three dimensional quadric

1996/08/21 by de Cataldo, Mark Andrea A.
#14E35 #14H45 #14M06 #14M07 #14M17 #14N99 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.alg-geom/9608019

Abstract

By means of an \it 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 2k, 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. Keywords: Castelnuovo-Harris Bound, Uniform Position Principle, Low Codimension, Linkage

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