Curves in the double plane

Details Curves in the double plane Curves in the double plane

1999-06-30

arxiv.org/abs/math/9906209v1

Mathematics

Algebraic Geometry

20 pages

Scientific paper

We study locally Cohen-Macaulay curves in projective three-space which are contained in a double plane 2H, thus completing the classification of curves lying on surfaces of degree two. We describe the irreducible components of the Hilbert schemes of locally Cohen-Macaulay curves in 2H of given degree and arithmetic genus. We show that these Hilbert schemes are connected. We also discuss the Rao modules of these curves, and liaison and biliaison equivalence classes.

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