Hilbert Schemes of Degree Four Curves

Scott Nollet; Enrico Schlesinger

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Hilbert Schemes of Degree Four Curves

Scott Nollet·Enrico Schlesinger

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Abstract

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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BibTeX RIS

Scott Nollet, Enrico Schlesinger. 2001-12-17. Hilbert Schemes of Degree Four Curves. https://arxiv.org/abs/math/0112167

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