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].
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Author information
Authors and Affiliations
Additional information
Received: 11 June 2001 / Revised version: 28 January 2002
Rights and permissions
About this article
Cite this article
Tziolas, N. Infinitesimal extensions of ℙ1 and their Hilbert schemes. Manuscripta Math. 108, 461–482 (2002). https://doi.org/10.1007/s002290200278
Issue Date:
DOI: https://doi.org/10.1007/s002290200278