Related papers: Monomial Cremona transformations and toric polar m…

We classify the homogeneous polynomials in three variables whose toric polar linear system defines a Cremona transformation. This classification also includes, as a proper subset, the classification of toric surface patches from geometric…

We compute the multidegrees and the Segre numbers of general determinantal Cremona transformations, with generically reduced base scheme, by specializing to the standard Cremona transformation and computing its Segre class via mixed volumes…

This article studies the possible degenerations of plane Cremona transformations of some degree into maps of smaller degree.

Suppose that X to Y is a generically finite map of nonsingular varieties over a field of characteristic zero, and v is a valuation of the function field of X. We prove that it is possible to perform a sequence of monoidal transforms X' to X…

We proved that, in characteristic 0, if two dominant endomorphisms of the projective plane of degree at least 2 are conjugate by some birational transformation, then they are conjugate by an automorphism. We also gave counterexamples in…

We define a bar construction endofunctor on the category of commutative augmented monoids $A$ of a symmetric monoidal category $\mathcal{V}$ endowed with a left adjoint monoidal functor $F:s\mathbf{Set}\to \mathcal{V}$. To do this, we need…

In this paper we will show that monomial summability can be characterized using Borel-Laplace like integral transformations depending of a parameter $0<s<1$. We will apply this result to prove 1-summability in a monomial of formal solutions…

From Smyth's classification, modular compactifications of pointed smooth rational curves are indexed by combinatorial data, so-called extremal assignments. We explore their combinatorial structures and show that any extremal assignment is a…

We show that the ordinal of the dynamical degrees of all complex birational maps of the projective plane is $\omega^\omega$.

In this paper, we develop several tools to study the degree growth and stabilization of monomial maps. Using these tools, we can classify semisimple three dimensional monomial maps by their dynamical behavior.

A birational map from a projective space onto a not too much singular projective variety with a single irreducible non-singular base locus scheme (special birational transformation) is a rare enough phenomenon to allow meaningful and…

Veneroni maps are a class of birational transformations of projective spaces. This class contains the classical Cremona transformation of the plane, the cubo-cubic transformation of the space and the quatro-quartic transformation of…

We prove that the lexicographic, degree lexicographic and the degree reverse lexicographic orders for monomials in $R_n=K[X_1,...X_n]$ are uniquely determined by their induced orderings, (i.e. their restrictions to $R_{n,i}=K[X_1,...,…

We prove a monomialization theorem for mappings in general classes of infinitely differentiable functions that are called quasianalytic. Examples include Denjoy-Carleman classes, the class of $\cC^\infty$ functions definable in a…

We present some (unfortunately not all) known properties on the Cremona group; when it's possible we mentioned links with the most known group of polynomial automorphisms of the affine plane. The mentioned properties are essentially…

We find all possible isomorphisms and 3-birational maps (i.e., birational maps which induce an isomorphism between open subsets whose respective complements have codimension at least 3) between moduli spaces of parabolic vector bundles with…

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…

Given a monoidal $\infty$-category $C$ equipped with a monoidal recollement, we give a simple criterion for an object in $C$ to be dualizable in terms of the dualizability of each of its factors and a projection formula relating them.…

Consider an n-dimensional projective toric variety X defined by a convex lattice polytope P. David Cox introduced the toric residue map given by a collection of n+1 divisors Z_0,...,Z_n on X. In the case when the Z_i are T-invariant…

We study the generating series associated with the degree sequence of a monomial self-map of a projective toric variety. We establish conditions under which this series has its circle of convergence as a natural boundary, and hence is a…