The genus of curves on the three dimensional quadric

Details The genus of curves on the three dimensional quadric The genus of curves on the three dimensional quadric

1996-08-21

arxiv.org/abs/alg-geom/9608019v1

Mathematics

Algebraic Geometry

Amsppt,15 pages, to appear in Nagoya Math. J

Scientific paper

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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