Infinitesimal Extensions of P^1 and their Hilbert Schemes
Algebraic Geometry
2009-09-25 v1
Abstract
In order to calculate the multiplicity of an isolated rational curve C in a local complete intersection variety X, i.e. the length 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 P^1 by locally free sheaves. In this paper we study infinitesimal extensions of P^1, determine their structure and obtain upper and lower bounds for the length of the local rings of their Hilbert schemes at [P^].
Keywords
Cite
@article{arxiv.math/0110083,
title = {Infinitesimal Extensions of P^1 and their Hilbert Schemes},
author = {Nikolaos Tziolas},
journal= {arXiv preprint arXiv:math/0110083},
year = {2009}
}
Comments
22 pages