Related papers: Les applications monomiales en deux dimensions
Looking at some monoids and (semi)rings (natural numbers, integers and p-adic integers), and more generally, residually finite algebras (in a strong sense), we prove the equivalence of two ways for a function on such an algebra to behave…
A sharp bound is obtained for the number of ways to express the monomial $X^n$ as a product of linear factors over $\mathbb{Z}/p^{\alpha}\mathbb{Z}$. The proof relies on an induction-on-scale procedure which is used to estimate the number…
In this article we apply results of \cite{W} on the twisted Mellin transform to problems in toric geometry. In particular we use these results to describe the asymptotics of probability densities associated with the monomial eigenstates,…
In this review, novel non-standard techniques for the computation of cohomology classes on toric varieties are summarized. After an introduction of the basic definitions and properties of toric geometry, we discuss a specific computational…
We investigate the logarithmic bundles associated to arrangements of hypersurfaces with a fixed degree in a smooth projective variety. We then specialize to the case when the variety is a quadric hypersurface and a multiprojective space to…
Motivated by recent results on the Waring problem for polynomial rings and representation of monomial as sum of powers of linear forms, we consider the problem of presenting monomials of degree kd as sums of k-th powers of forms of degree…
We show that bosonization in two dimensions can be derived as a special case of the duality transformations that have recently been used to good effect in string theory. This allows the construction of the bosonic counterpart of any…
We show how classical and quantum dualities, as well as duality relations that appear only in a sector of certain theories ("emergent dualities"), can be unveiled, and systematically established. Our method relies on the use of morphisms of…
We characterize embeddability of algebraic varieties into smooth toric varieties and prevarieties. Our embedding results hold also in an equivariant context and thus generalize a well known embedding theorem of Sumihiro on quasiprojective…
We provide the set of filters (saturated submonoids) in a commutative monoid with a topology (like the spectrum of a ring) and study the resulting spaces.
We describe the equivariant cobordism ring of smooth toric varieties. This equivariant description is used to compute the ordinary cobordism ring of such varieties.
We give an overview of invariants of algebraic singularities over perfect fields. We then show how they lead to a synthetic proof of embedded resolution of singularities of 2-dimensional schemes.
We associate a bivariant theory to any suitable oriented Borel-Moore homology theory on the category of algebraic schemes or the category of algebraic G-schemes. Applying this to the theory of algebraic cobordism yields operational…
Let X be a normal complex projective variety with at worst klt singularities, and L a big line bundle on X. We use valuations to study the log canonical threshold of L, as well as another invariant, the stability threshold. The latter…
The purpose of this paper is to study singular holomorphic foliations of arbitrary codimension defined by logarithmic forms on projective spaces.
Although algebraic structures are frequently analyzed using unary and binary operations, they can also be effectively defined and unified through ternary operations. In this context, we introduce structures that contain two constants and a…
This note proves the existence of universal rational parametrizations. The description involves homogeneous coordinates on a toric variety coming from a lattice polytope. We first describe how smooth toric varieties lead to universal…
We give a combinatorial algorithm for equivariant embedded resolution of singularities of a toric variety defined over a perfect field. The algorithm is realized by a finite succession of blowings-up with smooth invariant centres that…
In this paper, we classify smooth, contractible affine varieties equipped with faithful torus actions of complexity two, having a unique fixed point and a two-dimensional algebraic quotient isomorphic to a toric blow-up of a toric surface.…
In this paper we build an Orlik-Solomon model for the canonical gradation of the cohomology algebra with integer coefficients of the complement of a toric arrangement. We give some results on the uniqueness of the representation of…