Hilbert Schemes of Degree Four Curves

Preprint

17 December 2001

preprint
Published by arXiv in arXiv

https://doi.org/10.48550/arXiv.math/0112167

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.

Keywords

IRREDUCIBLE COMPONENTS
ARBITRARY ARITHMETIC
DEGREE FOUR CURVES
ARITHMETIC GENUS
HILBERT SCHEMES
SPACE CURVES
FOUR CURVES

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