Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Rational curves of degree at most 9 on a general quintic threefold   We prove the following form of the Clemens conjecture in low degree. Let
$d\le9$, and let $F$ be a general quintic threefold in $\IP^4$. Then (1)~the
Hilbert scheme of rational, smooth and irreducible curves of degree $d$ on $F$
is finite, nonempty, and reduced; moreover, each curve is embedded in $F$ with
normal bundle $\O(-1)\oplus\O(-1)$, and in $\IP^4$ with maximal rank. (2)~On
$F$, there are no rational, singular, reduced and irreducible curves of degree
$d$, except for the 17,601,000 six-nodal plane quintics (found by Vainsencher).
(3)~On $F$, there are no connected, reduced and reducible curves of degree $d$
with rational components.

22
The categories of this paper are: chao-dyn
29
The categories of this paper are: funct-an
23
The categories of this paper are: solv-int
9
The categories of this paper are: nlin
10
The categories of this paper are: q-bio
16
The categories of this paper are: stat
6
The categories of this paper are: astro-ph
1
The categories of this paper are: cs
17
The categories of this paper are: q-fin
20
The categories of this paper are: acc-phys
33
The categories of this paper are: plasm-ph
31
The categories of this paper are: ao-sci
26
The categories of this paper are: bayes-an
32
The categories of this paper are: atom-ph
35
The categories of this paper are: mtrl-th
24
The categories of this paper are: dg-ga