Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Obstructions to deforming space curves and non-reduced components of the
  Hilbert scheme   Let $Hilb P^3$ denote the Hilbert scheme of smooth connected curves in $P^3$.
We consider maximal irreducible closed subsets $W \subset Hilb P^3$ whose
general member $C$ is contained in a smooth cubic surface and investigate the
conditions for $W$ to be a component of $(Hilb P^3)_{red}$. We especially study
the case where the dimension of the tangent space of $Hilb P^3$ at $[C]$ is
greater than $\dim W$ by one. We compute obstructions to deforming $C$ in $P^3$
and prove that for every $W$ in this case, $Hilb P^3$ is non-reduced along $W$
and $W$ is a component of $(Hilb P^3)_{red}$.

26
The categories of this paper are: bayes-an
31
The categories of this paper are: ao-sci
1
The categories of this paper are: cs
12
The categories of this paper are: nucl-th
3
The categories of this paper are: physics
25
The categories of this paper are: patt-sol
4
The categories of this paper are: cond-mat
19
The categories of this paper are: eess
8
The categories of this paper are: hep-ex
33
The categories of this paper are: plasm-ph
32
The categories of this paper are: atom-ph
6
The categories of this paper are: astro-ph
5
The categories of this paper are: gr-qc
17
The categories of this paper are: q-fin
15
The categories of this paper are: nucl-ex
13
The categories of this paper are: quant-ph