Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Obstructions to deforming curves on an Enriques-Fano 3-fold   We study the deformations of a curve $C$ on an Enriques-Fano $3$-fold $X
\subset \mathbb P^n$, assuming that $C$ is contained in a smooth hyperplane
section $S \subset X$, that is a smooth Enriques surface in $X$. We give a
sufficient condition for $C$ to be (un)obstructed in $X$, in terms of half
pencils and $(-2)$-curves on $S$. Let $\operatorname{Hilb}^{sc} X$ denote the
Hilbert scheme of smooth connected curves in $X$. By using the Hilbert-flag
scheme of $X$, we also compute the dimension of $\operatorname{Hilb}^{sc} X$ at
$[C]$ and give a sufficient condition for $\operatorname{Hilb}^{sc} X$ to
contain a generically non-reduced irreducible component of Mumford type.

12
The categories of this paper are: nucl-th
22
The categories of this paper are: chao-dyn
26
The categories of this paper are: bayes-an
37
The categories of this paper are: supr-con
24
The categories of this paper are: dg-ga
5
The categories of this paper are: gr-qc
20
The categories of this paper are: acc-phys
25
The categories of this paper are: patt-sol
13
The categories of this paper are: quant-ph
1
The categories of this paper are: cs
8
The categories of this paper are: hep-ex
36
The categories of this paper are: cmp-lg
10
The categories of this paper are: q-bio
15
The categories of this paper are: nucl-ex
0
The categories of this paper are: hep-ph
32
The categories of this paper are: atom-ph