Abstract
In order to calculate the multiplicity of an isolated rational curve C on a local complete intersection variety X, i.e. the length of the local ring of the Hilbert Scheme of X at [C], it is important to study infinitesimal neighborhoods of the curve in X. This is equivalent to infinitesimal extensions of ℙ1 by locally free sheaves. In this paper we study infinitesimal extensions of ℙ1, determine their structure and obtain upper and lower bounds for the length of the local rings of their Hilbert schemes at [ℙ1].
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