Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Infinitesimal Extensions of P^1 and their Hilbert Schemes   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^].

27
The categories of this paper are: comp-gas
20
The categories of this paper are: acc-phys
23
The categories of this paper are: solv-int
5
The categories of this paper are: gr-qc
26
The categories of this paper are: bayes-an
8
The categories of this paper are: hep-ex
36
The categories of this paper are: cmp-lg
13
The categories of this paper are: quant-ph
11
The categories of this paper are: hep-lat
15
The categories of this paper are: nucl-ex
3
The categories of this paper are: physics
18
The categories of this paper are: econ
31
The categories of this paper are: ao-sci
14
The categories of this paper are: math-ph
22
The categories of this paper are: chao-dyn
12
The categories of this paper are: nucl-th