Related papers: Finite subgroups of the plane Cremona group
We classify, up to conjugacy, the subgroups of the Cremona group isomorphic to (Z/p)^r, where p is prime and r is maximal.
We give a sharp bound for orders of elementary abelian 2-groups of birational automorphisms of rationally connected threefolds.
In this work, we study a family of Cremona transformations of weighted projective planes which generalize the standard Cremona transformation of the projective plane. Starting from special plane projective curves we construct families of…
We give a complete solution of the linearization problem in the plane Cremona group over an algebraically closed field of characteristic zero.
We use a recent advance in birational geometry to prove new lower bounds on the essential dimension of some finite groups.
This article studies the possible degenerations of plane Cremona transformations of some degree into maps of smaller degree.
We classify all monomial planar Cremona maps by multidegree using recent methods developed by Aluffi. Following the main result, we prove several more properties of the set of these maps, and also extend the results to the more general…
Let $\mathbf{K}$ be an algebraically closed field. The Cremona group $\operatorname{Cr}_2(\mathbf{K})$ is the group of birational transformations of the projective plane $\mathbb{P}^2_{\mathbf{K}}$. We carry out an overall study of…
We give an explicit set of generators for various natural subgroups of the real Cremona group Bir_R(P^2). This completes and unifies former results by several authors.
We compute the presentations of fundamental groups of the complements of a class of rational cuspidal projective plane curves classified by Flenner, Zaidenberg, Fenske and Saito. We use the Zariski-Van Kampen algorithm and exploit the…
We prove that over any perfect field the plane Cremona group is generated by involutions.
For perfect fields $k$ satisfying $[\bar k:k]>2$, we construct new normal subgroups of the plane Cremona group and provide an elementary proof of its non-simplicity, following the melody of the recent proof by Blanc, Lamy and Zimmermann…
In the paper it is proven that Carter subgroups of a finite group are conjugate. A complete classification of Carter subgroups in finite almost simple groups is also obtained.
This article studies the group generated by automorphisms of the projective space of dimension $n$ and by the standard birational involution of degree $n$. Every element of this group only contracts rational hypersurfaces, but in odd…
We give a simple set of generators and relations for the Cremona group of the plane. Namely, we show that the Cremona group is the amalgamated product of the de Jonqui\`eres group with the group of automorphisms of the plane, divided by one…
We give an explicit bound on orders of finite subgroups of Cremona group of rank three over $\mathbb{Q}$.
We study the birational self-maps of the projective plane over finite fields that induce permutations on the set of rational points. As a main result, we prove that no odd permutation arises over a non-prime finite field of characteristic…
A classical result asserts that the complex projective plane modulo complex conjugation is the 4-dimensional sphere. We generalize this result in two directions by considering the projective planes over the normed real division algebras and…
Since the end of the XIXth century, we know that each birational map of the complex projective plane is the product of a finite number of quadratic birational maps of the projective plane; this motivates our work which essentially deals…
It is well known that all Borel subgroups of a linear algebraic group are conjugate. This result also holds for the automorphism group ${{\mathrm{Aut}}} (\mathbb A^2)$ of the affine plane \cite{BerestEshmatovEshmatov2016} (see also…