Related papers: On degenerations of plane Cremona transformations

The theory of modular deformations is generalized for the category of complex analytic polyhedra which includes germs of complex space as well as any compact complex analytic space. The objective of the theory is a construction of fine…

In this paper, we extend the method developed in [17, 18] to curves in the Minkowski plane. The method proposes a way to study deformations of plane curves taking into consideration their geometry as well as their singularities. We deal in…

We study the quasi-projective variety Bir_d of plane Cremona transformations defined by three polynomials of fixed degree d and its subvariety Bir_d^o where the three polynomials have no common factor. We compute their dimension and the…

We discuss the concept of Cremona contractible plane curves, with an historical account on the development of this subject. We then classify Cremona contractible unions of d > 11 lines in the plane.

An algebraic deformation theory of module-algebras over a bialgebra is constructed. The cases of module-coalgebras, comodule-algebras, and comodule-coalgebras are also considered.

In a series of papers, Aluffi and Faber computed the degree of the $GL_3$ orbit closure of an arbitrary plane curve. We attempt to generalize this to the equivariant setting by studying how orbits degenerate under some natural…

This paper focuses on a new approach to plane geometry and develops important concepts that can allow researchers to unite and observe plane geometry from a new, meaningful perspective.

In this note we collect some results on the deformation theory of toric Fano varieties.

This article deals with the study of the birational transformations of the projective complex plane which leave invariant an irreducible algebraic curve. We try to describe the state of art and provide some new results on this subject.

In this paper we describe conjugacy classes of finite subgroups of odd order in the group of birational automorphisms of the real projective plane.

This paper surveys and gives a uniform exposition of results contained in papers published by the team of authors. The subject is degenerations of surfaces, especially to unions of planes. More specifically, we deduce some properties of the…

We study deformations of complex projective varieties that are homotopically or homologically trivial. We formulate several conjectures and give some examples and partial answers.

We show that monomial Cremona maps of degree d on P^n can have inverses whose degree d' is quite large (for d > 2, d' = ((d-1)^n - 1)/(d-2) occurs), and that the full list of degrees d' does not always form an interval. An easy method for…

In this article we construct a specific projective degeneration of K3 surfaces of degree 2g-2 in P^g to a union of 2g-2 planes, which meet in such a way that the combinatorics of the configuration of planes is a triangulation of the…

This paper contains a new proof of the classification of elements of prime order in the Cremona group Bir(P^2), up to conjugation. In addition, we give explicit geometric constructions of these Cremona transformations, and provide a…

This survey deals with the Cremona group via its subgroups.

An algebraic deformation theory of dialgebra morphisms is obtained.

In this note we describe the embeddings of the Heisenberg group into the Cremona group.

An algebraic deformation theory of morphisms of dual Leibniz algebras is obtained.

This is the paper as published. The topology of a complex plane curve singularity with real branches is deduced from any real deformation having delta crossings. An example of the computation of the global geometric monodromy of a…