Related papers: Equivalent birational embeddings

In this paper we prove a higher dimensional analogue of Carleson's $\varepsilon^2$ conjecture. Given two arbitrary disjoint open sets $\Omega^+,\Omega^-\subset \mathbb{R}^{n+1}$, and $x\in\mathbb{R}^{n+1}$, $r>0$, we denote…

For point $x$ in the inverse limit space $X$ with a single unimodal bonding map we construct, with the use of symbolic dynamics, a planar embedding such that $x$ is accessible. It follows that there are uncountably many non-equivalent…

In this paper, we first present combinatorial proofs of a kind of expansions of the Eulerian polynomials of types A and B, and then we introduce Stirling permutations of the second kind. In particular, we count Stirling permutations of the…

We give a sharp bound for orders of elementary abelian 2-groups of birational automorphisms of rationally connected threefolds.

It is well known that there exists a significant equivalence between the vector space $\mathbb{F}_{q}^n$ and the finite fields $\mathbb{F}_{q^n}$, and many scholars often view them as the same in most contexts. However, the precise…

Let $V$ be a left vector space over a division ring and let ${\mathcal P}(V)$ be the associated projective space. We describe all finite subsets $X\subset V$ such that every permutation on $X$ can be extended to a linear automorphism of $V$…

In this paper certain $n$-dimensional inequalities are shown to be equivalent to the inequalities in the one-dimensional setting. By this means, embeddings between weighted local Morrey-type spaces are characterized for some ranges of…

We prove that each semialgebraic subset of $\R^n$ of positive codimension can be locally approximated of any order by means of an algebraic set of the same dimension. As a consequence of previous results, algebraic approximation preserving…

Let $A$ be an algebra over a commutative ring $k$. We prove that braidings on the category of $A$-bimodules are in bijective correspondence to canonical R-matrices, these are elements in $A\ot A\ot A$ satisfying certain axioms. We show that…

Let $X$ be a smooth projective variety of Albanese fiber dimension 1 and of general type. We prove that the translates through 0 of all components of $V^0(\omega_X)$ generate $\Pic^0(X)$. We then study the pluricanonical maps of $X$. We…

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 prove that any closed map between metrizable spaces can be extended to a closed map between completely metrizable spaces with the same extensional dimension.

We produce refinements of the known multiplicative structures on the Brown--Peterson spectrum $BP$, its truncated variants $BP\langle n \rangle$, Ravenel's spectra $X(n)$, and evenly graded polynomial rings over the sphere spectrum.…

We prove a sharp Bernstein-type inequality for complex polynomials which are positive and satisfy a polynomial growth condition on the positive real axis. This leads to an improved upper estimate in the recent work of Culiuc and Treil on…

We use a double degeneration technique to calculate the dimension of the secant variety of any Segre-Veronese embedding of (P^1)^r

Given a geometrically irreducible subscheme X in P^n over F_q of dimension at least 2, we prove that the fraction of degree d hypersurfaces H such that the intersection of H and X is geometrically irreducible tends to 1 as d tends to…

We study the combinatorial equivalence of separable elements in types $A$ and $B$. A bijection is constructed from the set of separable permutations in the symmetric group $S_{n+1}$ to the set of separable signed permutations in the…

Vertex algebras are equivalent to translation-equivariant chiral algebras on $\mathbb{A}^1$, in the sense of Beilinson and Drinfeld. In this paper we give an algebraic construction of a chiral algebra on $\mathbb{A}^n$; this can be seen as…

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…

Let $(X, d)$ be a semimetric space. A permutation $\Phi$ of the set $X$ is a combinatorial self similarity of $(X, d)$ if there is a bijective function $f \colon d(X^2) \to d(X^2)$ such that $$ d(x, y) = f(d(\Phi(x), \Phi(y))) $$ for all…