Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the Hilbert scheme of smooth curves in $\mathbb{P}^4$ of degree $d =
  g+1$ and genus $g$ with negative Brill-Noether number   We denote by $\mathcal{H}_{d,g,r}$ the Hilbert scheme of smooth curves, which
is the union of components whose general point corresponds to a smooth
irreducible and non-degenerate curve of degree $d$ and genus $g$ in $\PP^r$. In
this article, we show that for low genus $g$ outside the Brill-Noether range,
the Hilbert scheme $\mathcal{H}_{g+1,g,4}$ is non-empty whenever $g\ge 9$ and
irreducible whose only component generically consists of linearly normal curves
unless $g=9$ or $g=12$. This complements the validity of the original assertion
of Severi regarding the irreducibility of $\mathcal{H}_{d,g,r}$ outside the
Brill-Nother range for $d=g+1$ and $r=4$.

21
The categories of this paper are: adap-org
31
The categories of this paper are: ao-sci
12
The categories of this paper are: nucl-th
18
The categories of this paper are: econ
6
The categories of this paper are: astro-ph
14
The categories of this paper are: math-ph
5
The categories of this paper are: gr-qc
22
The categories of this paper are: chao-dyn
35
The categories of this paper are: mtrl-th
33
The categories of this paper are: plasm-ph
34
The categories of this paper are: chem-ph
16
The categories of this paper are: stat
24
The categories of this paper are: dg-ga
15
The categories of this paper are: nucl-ex
28
The categories of this paper are: alg-geom
25
The categories of this paper are: patt-sol