Related papers: A generalized Gaeta's Theorem

We give criteria for R-equivalence of torsors under finite constant group schemes over a field. In paticular, using bitorsors, we obtain a Galois devissage result which formalises and generalises a theorem of Philippe Gille in the case of…

We generalize the definition of the polylogarithm classes to the case of commutative group schemes, both in the sheaf theoretic and the motivic setting. This generalizes and simplifies the existing cases.

We define and explicitly construct schemes evinced by generalized additive decompositions (GADs) of a given $d$-homogeneous polynomial $F$. We employ GADs to investigate the regularity of $0$-dimensional schemes apolar to $F$, focusing on…

We define the Grothendieck-Witt category over a fixed ground ring. In order to study the structure of this category, we introduce the general theory of Gysin functors and their associated categories of correspondences. The latter…

In matching theory, barrier sets (also known as Tutte sets) have been studied extensively due to its connection to maximum matchings in a graph. In this paper, we first define $\theta$-barrier sets. Our definition of a $\theta$-barrier set…

Let $t$ be a fixed parameter and $x$ some indeterminate. We give some properties of the generalized binomial coefficients $\genfrac{<}{>}{0pt}{}{x}{k}$ inductively defined by $k/x \genfrac{<}{>}{0pt}{}{x}{k}=…

Applying E. Kowalski's recent generalization of the large sieve we prove that certain properties expected to be typical (irreducibility of the characteristic polynomial, absence of squares among the matrix coefficients...) are indeed…

We study generic holomorphic families of dynamical systems presenting problems of small divisors with fixed arithmetic. We prove that we have convergence for all parameter values or divergence everywhere except for an exceptional set in the…

A more general class than complete intersection singularities is the class of determinantal singularities. They are defined by the vanishing of all the minors of a certain size of a $m\times n$-matrix. In this note, we consider…

We establish sharp estimates that adapt the polynomial method to arbitrary varieties. These include a partitioning theorem, estimates on polynomials vanishing on fixed sets and bounds for the number of connected components of real algebraic…

Taking symmetric powers of varieties can be seen as a functor from the category of varieties to the category of varieties with an action by the symmetric group. We study a corresponding map between the Grothendieck groups of these…

A hierarchy of matrix-valued polynomials which generalize the Jacobi polynomials is found. Defined by a Rodrigues formula, they are also products of a sequence of differential operators. Each class of polynomials is complete, satisfies a…

Starting with the zero-square "zeon algebra" the connection with permanents is shown. Permanents of sub-matrices of a linear combination of the identity matrix and all-ones matrix leads to moment polynomials with respect to the exponential…

We generalize Coincidence theorem due to Walsh for symmetric and linear polynomial in n complex variables, that is linear in each of them having total degre n. We discuss case when total degree is smaller then n. This case has been already…

From the generating matrix of a linear code one can construct a sequence of generalized star configurations which are strongly connected to the generalized Hamming weights and the underlying matroid of the code. When the code is MDS, the…

Let G be a finite group acting linearly on the polynomial ring with invariant ring R. If the action is small, then a classical result of Auslander gives in dimension two a correspondence between linear representations of G and maximal…

Kobayashi-Ochiai's theorem says us that the set of dominant rational maps to a complex variety of general type is finite. In this paper, we give a generalization of it in the category of log schemes.

We consider the problem of deciding if a set of quantum one-qudit gates $\mathcal{S}=\{g_1,\ldots,g_n\}\subset G$ is universal, i.e if the closure $\overline{<\mathcal{S}>}$ is equal to $G$, where $G$ is either the special unitary or the…

The development of mathematics has been characterized by the increasing interconnectivity of seemingly separate disciplines. Such interplay has been facilitated by a massive development in formalism; category theory has provided a common…

We present sweeping line graphs, a generalization of $\Theta$-graphs. We show that these graphs are spanners of the complete graph, as well as of the visibility graph when line segment constraints or polygonal obstacles are considered. Our…