Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Cremona maps and involutions   We deal with the following question of Dolgachev : is the Cremona group
generated by involutions ? Answer is yes in dimension $2$ (Cerveau-Deserti). We
give an upper bound of the minimal number $\mathfrak{n}_\varphi$ of involutions
we need to write a birational self map $\varphi$ of $\mathbb{P}^2_\mathbb{C}$.
  We prove that de Jonqui\`eres maps of $\mathbb{P}^3_\mathbb{C}$ and maps of
small bidegree of $\mathbb{P}^3_\mathbb{C}$ can be written as a composition of
involutions of $\mathbb{P}^3_\mathbb{C}$ and give an upper bound of
$\mathfrak{n}_\varphi$ for such maps $\varphi$. We get similar results in
particular for automorphisms of $(\mathbb{P}^1_\mathbb{C})^n$, automorphisms of
$\mathbb{P}^n_\mathbb{C}$, tame automorphisms of $\mathbb{C}^n$, monomial maps
of $\mathbb{P}^n_\mathbb{C}$, and elements of the subgroup generated by the
standard involution of $\mathbb{P}^n_\mathbb{C}$ and
$\mathrm{PGL}(n+1,\mathbb{C})$.

20
The categories of this paper are: acc-phys
1
The categories of this paper are: cs
16
The categories of this paper are: stat
24
The categories of this paper are: dg-ga
37
The categories of this paper are: supr-con
4
The categories of this paper are: cond-mat
7
The categories of this paper are: hep-th
6
The categories of this paper are: astro-ph
0
The categories of this paper are: hep-ph
28
The categories of this paper are: alg-geom
18
The categories of this paper are: econ
29
The categories of this paper are: funct-an
10
The categories of this paper are: q-bio
33
The categories of this paper are: plasm-ph
13
The categories of this paper are: quant-ph
12
The categories of this paper are: nucl-th