Related papers: On degenerations of plane Cremona transformations

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…

We give a fine classification of cubic plane Cremona maps. A previous partial classification was obtained by Cerveau and D\'eserti a few years ago.

One studies Cremona monomial maps by combinatorial means. Among the results is a simple integer matrix theoretic proof that the inverse of a Cremona monomial map is also defined by monomials of fixed degree, and moreover, the set of…

This paper is concerned with suitable generalizations of a plane de Jonqui\`eres map to higher dimensional space $\mathbb{P}^n$ with $n\geq 3$. For each given point of $\mathbb{P}^n$ there is a subgroup of the entire Cremona group of…

The main purpose of this paper is to study formal deformations of evolution algebras, determining their existence and classifying them up to equivalence. In addition, we examine degenerations in this setting and provide Hasse diagrams that…

We construct Cremona transformations of P^3 with bidegrees (d,e), where d<e^2+1, e< d^2+1 and d,e> 0.

Survey article on the geometry of spherical varieties. Invited survey for Transformation Groups.

We study the plane automorphisms given by polynomials with certain degree decompositions.

We present the abelianisation of the birational transformations of the real projective plane.

We apply the results of arXiv:1109.3573 to study quadro-quadric Cremona transformations in low-dimensional projective spaces. In particular we describe new very simple families of such birational maps and obtain complete and explicit…

In this paper we study the degeneration of convex real projective structures on bordered surfaces.

In this article, we study birational transformations belonging to Galois points for certain plane quartic curve. In fact, we see that they can be extended to Cremona transformations. In particular, we determine the conjugacy class of them.…

We study automorphism groups of real del Pezzo surfaces, concentrating on finite groups acting minimally on them. As a result, we obtain a vast part of classification of finite subgroups in the real plane Cremona group.

The aim of this paper is to give a finer geometric description of the algebraic varieties parametrizing conjugacy classes of nonsolvable subgroups in the plane Cremona group.

An algebraic deformation theory of coalgebra morphisms is constructed.

In this paper we study degenerations of scrolls to union of planes, a problem already considered by G. Zappa in 1940-50. We prove, using techniques different from the ones of Zappa, a degeneration result to union of planes with the mildest…

Cremona maps defined by monomials of degree 2 are thoroughly analyzed and classified via integer arithmetic and graph combinatorics. In particular, the structure of the inverse map to such a monomial Cremona map is made very explicit as is…

A generalization of the plane de Jonqui\`eres transformation to arbitrary dimension is studied, with an eye for the ideal theoretic side. In particular, one considers structural properties of the corresponding base ideal and of its defining…

We investigate the problem of existence of degenerations of surfaces in $\mathbb P^3$ with ordinary singularities into plane arrangements in general position.

We provide a description of W_3 transformations in terms of deformations of convex curves in two dimensional Euclidean space. This geometrical interpretation sheds some light on the nature of finite W_3-morphisms. We also comment on how…