Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The action of the Cremona group on rational curves of $ \mathbb{P}^{3} $   A Cremona transformation is a birational self-map of the projective space $
\mathbb{P}^{n} $. Cremona transformations of $ \mathbb{P}^{n} $ form a group
and this group has a rational action on subvarieties of $ \mathbb{P}^{n} $ and
hence on its Hilbert scheme. We study this action on the family of rational
curves of $ \mathbb{P}^{3} $ and we prove the rectifiability of any one
dimensional family. This shows that any uniruled surface is Cremona equivalent
to a scroll and it answers a question of Bogomolov-B\"ohning related to the
study of uniformly rational varieties. We provide examples of infinitely many
scrolls in the same Cremona orbit and we show that a "general" scroll is not in
the Cremona orbit of a "general" rational surface.

21
The categories of this paper are: adap-org
17
The categories of this paper are: q-fin
30
The categories of this paper are: q-alg
37
The categories of this paper are: supr-con
6
The categories of this paper are: astro-ph
0
The categories of this paper are: hep-ph
29
The categories of this paper are: funct-an
3
The categories of this paper are: physics
27
The categories of this paper are: comp-gas
34
The categories of this paper are: chem-ph
4
The categories of this paper are: cond-mat
26
The categories of this paper are: bayes-an
11
The categories of this paper are: hep-lat
36
The categories of this paper are: cmp-lg
24
The categories of this paper are: dg-ga
9
The categories of this paper are: nlin