Related papers: On degenerations of plane Cremona transformations

In this paper, a geometric interpretation is provided of a new rational Landen transformation. The convergence of its iterates is also established.

The goal of this paper is to develop some aspects of the deformation theory of piecewise flat structures on surfaces and use this theory to construct new geometric structures on the moduli space of Riemann surfaces.

Proton decay is a hypothetical form of particle decay in which protons are assumed to decay into lighter particles. This form of decay has yet to be detected. In this contribution to the proceedings of Neutrino 2022, we review the current…

We classify endomorphisms of the plane that preserve a pencil of curves.

The aim of this paper is to study the degenerate Bell numbers and polynomials which are degenerate version of the Bell numbers and polynomials. we derive some new identities and properties of those numbers and polynomials that are…

This article is a survey of results involving conformal deformation of Riemannian metrics and fully nonlinear equations.

We prove that over any perfect field the plane Cremona group is generated by involutions.

This is a survey on recent results on the Loewner theory in one and several complex manifolds

We obtain a sharp bound for p-elementary subgroups in the plane Cremona group over an arbitrary perfect field.

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…

This article follows and completes [arXiv:2511.14222], where we study the problem of bounded deviations for homeomorphisms of closed surfaces of genus $\ge 2$. This second part deals with bounded deviations relative to geodesic minimal…

This paper is an adaptation of a chapter from an upcoming monograph on noncommutative geometry and quantum groups. We present examples of non compact quantum groups which are deformations of low dimensional Lie groups. The paper is of…

In this article we study devlop some fundaments for a function theory in the 16-dimensional complexified octonions.

Recent developments on the uniformity of the number of rational points on curves and subvarieties in a moving abelian variety rely on the geometric concept of the degeneracy locus. The first-named author investigated the degeneracy locus in…

Planar polynomial automorphisms are polynomial maps of the plane whose inverse is also a polynomial map. A map is reversible if it is conjugate to its inverse. Here we obtain a normal form for automorphisms that are reversible by an…

We study the Farrell and Jones Warping Deformation.

This paper is based on a course given by the author at the University of Rome ``La Sapienza'' in the Academic year 2000/2001. The intended aim of the course was to rapidly introduce, although not in an exhaustive way, the non-expert PhD…

Degenerations of Lie algebras of meromorphic vector fields on elliptic curves (i.e. complex tori) which are holomorphic outside a certain set of points (markings) are studied. By an algebraic geometric degeneration process certain…

The aim of this paper is to report on recent development on the conformal fractional Laplacian, both from the analytic and geometric points of view, but especially towards the PDE community.

Complementing results of Hacking and Prokhorov, we determine in an explicit manner all log terminal, rational, degenerations of the projective plane that allow a non-trivial torus action.