Hilbert Schemes of Degree Four Curves

Details Hilbert Schemes of Degree Four Curves Hilbert Schemes of Degree Four Curves

2001-12-17

arxiv.org/abs/math/0112167v1

Compositio Math. 139 (2003), no. 2, 169--196

Mathematics

Algebraic Geometry

26 pages, no figures

Scientific paper

In this paper we determine the irreducible components of the Hilbert schemes H(4,g) of locally Cohen-Macaulay space curves of degree four and arbitrary arithmetic genus g. We show that these Hilbert schemes are connected, in spite of having about g^2/24 irreducible components. For g < -2 we exhibit a component that is disjoint from the component of extremal curves and use this to give a counterexample to a conjecture of Ait-Amrane and Perrin.

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