Related papers: Local Strong Factorization of birational maps

We study Abhyankar valuations of excellent equicharacteristic local domains with an algebraically closed residue field. For zero dimensional valuations we prove that whenever the ring is complete and the semigroup of values taken by the…

We show that branched coverings of surfaces of large enough genus arise as characteristic maps of braided surfaces that is, lift to embeddings in the product of the surface with $\mathbb R^2$. This result is nontrivial already for…

A smooth scheme X over a field k of positive characteristic is said to be strongly liftable, if X and all prime divisors on X can be lifted simultaneously over W_2(k). In this paper, first we prove that smooth toric varieties are strongly…

We give a short proof of the Zariski-Lipman conjecture for toric varieties: any complex toric variety with locally free tangent sheaf is smooth.

Given a rational monomial map, we consider the question of finding a toric variety on which it is algebraically stable. We give conditions for when such variety does or does not exist. We also obtain several precise estimates of the degree…

This note gives a unifying characterization and exposition of strongly irreducible elements and their duals in lattices. The interest in the study of strong irreducibility stems from commutative ring theory, while the dual concept of strong…

In Proposition I of "Memoire sur les conditions de resolubilite des equations par radicaux", Galois established that any intermediate extension of the splitting field of a polynomial with rational coefficients is the fixed field of its…

We determine a strong form of the decomposition theorem for proper toric maps over finite fields.

We show that algebraic formulas and constant-depth circuits are closed under taking factors. In other words, we show that if a multivariate polynomial over a field of characteristic zero has a small constant-depth circuit or formula, then…

We show that any separated essentially finite-type map $f$ of noetherian schemes globally factors as $f = hi$ where $i$ is an injective localization map and $h$ a separated finite-type map. In particular, via Nagata's compactification…

Starting from $\mathbb{C}^*$-actions on complex projective varieties, we construct and investigate birational maps among the corresponding extremal fixed point components. We study the case in which such birational maps are locally…

A proof is given that hard-scattering factorization is valid for deep-inelastic processes which are diffractive or which have some other condition imposed on the final state in the target fragmentation region.

A super-conformal map and a minimal surface are factored into a product of two maps by modeling the Euclidean four-space and the complex Euclidean plane on the set of all quaternions. One of these two maps is a holomorphic map or a…

The factorization of soft and ultrasoft gluons from collinear particles is shown at the level of operators in an effective field theory. Exclusive hadronic factorization and inclusive partonic factorization follow as special cases. The…

Let k be a field of characteristic zero, K an algebraic function field over k, and V a k-valuation ring of K. Zariski's theorem of local uniformization shows that there exist algebraic regular local rings R_i with quotient field K which are…

Building on his reduction to the case of an unramified complete regular local ring R of mixed characteristic, we propose a proof in the framework of P. Scholze's perfectoid theory. The main ingredients are the perfectoid "Abhyankar lemma"…

We address two longstanding open problems, one originating in PL topology, another in birational geometry. First, we prove the weighted version of Oda's \emph{strong factorization conjecture} (1978), and prove that every two birational…

Let k be an algebraically closed field of characteristic 0 and let K*/K be a finite extension of algebraic function fields of transcendence degree 2 over k. Let v* be a k-valuation of K* with valuation ring V* and let v be the restriction…

We give a constructive proof of the factorization theorem for the classical Hardy space in terms of fractional integral operator. Moreover, the result is extended to the multilinear case and weighted case. As an application, we obtain the…

We introduce the notion of quantum duplicates of an (associative, unital) algebra, motivated by the problem of constructing toy-models for quantizations of certain configuration spaces in quantum mechanics. The proposed (algebraic) model…