Related papers: A numerical criterion for simultaneous normalizati…
The multigraded Hilbert scheme parametrizes all homogeneous ideals in a polynomial ring graded by an abelian group with a fixed Hilbert function. We prove that any multigraded Hilbert scheme is smooth and irreducible when the polynomial…
In this article we review how categorical equivalences are realized by renormalization group flow in physical realizations of stacks, derived categories, and derived schemes. We begin by reviewing the physical realization of sigma models on…
Quot schemes of quotients of a trivial bundle of arbitrary rank on a nonsingular projective surface X carry perfect obstruction theories and virtual fundamental classes whenever the quotient sheaf has at most 1-dimensional support. The…
In this paper we study scalar multivariate subdivision schemes with general integer expanding dilation matrix. Our main result yields simple algebraic conditions on the symbols of such schemes that characterize their polynomial…
Given a finite group scheme $G$ over a field and a $G$-variety $X$, we obtain a criterion for $X$ to be $G$-normal in the sense of \cite{Br24}. When $G$ is diagonalizable, we describe the local structure of $G$-normal varieties in…
The $R_{\sigma,t}$-transform introduced by Bassa and Menares can be used to construct families of irreducible polynomials in $\mathbb{F}_q[x]$. This iterative construction is a generalization of Cohen's $R$-transform. For this transform,…
It is shown that, under suitable conditions, involving in particular the existence of analytic constants of motion, the presence of Lie point symmetries can ensure the convergence of the transformation taking a vector field (or dynamical…
Let $X$ be any rational surface. We construct a tilting bundle $T$ on $X$. Moreover, we can choose $T$ in such way that its endomorphism algebra is quasi-hereditary. In particular, the bounded derived category of coherent sheaves on $X$ is…
Our goal is to develop a general strategy to decompose a random variable $X$ into multiple independent random variables, without sacrificing any information about unknown parameters. A recent paper showed that for some well-known natural…
The subject of features normalization plays an important central role in data representation, characterization, visualization, analysis, comparison, classification, and modeling, as it can substantially influence and be influenced by all of…
Let X,Y be projective schemes over a discrete valuation ring R, where Y is generically smooth and g:X \to Y a surjective R-morphism such that g_*\mathcal{O}_X = \mathcal{O}_Y. We show that if the family X \to Spec(R) is isotrivial, then the…
Normalizing flows have shown great promise for modelling flexible probability distributions in a computationally tractable way. However, whilst data is often naturally described on Riemannian manifolds such as spheres, torii, and hyperbolic…
For any nonconstant f,g in C(x) such that the numerator H(x,y) of f(x)-g(y) is irreducible, we compute the genus of the normalization of the curve H(x,y)=0. We also prove an analogous formula in arbitrary characteristic when f and g have no…
In this paper, we present a unified analysis of matrix completion under general low-dimensional structural constraints induced by {\em any} norm regularization. We consider two estimators for the general problem of structured matrix…
In this paper we provide a new method to certify that a nearby polynomial system has a singular isolated root with a prescribed multiplicity structure. More precisely, given a polynomial system f $=(f\_1, \ldots, f\_N)\in C[x\_1, \ldots,…
In two previous papers we showed that any analytically integrable vector field admits a local analytic Poincar\'e-Birkhoff normalization in the neighborhood of a singular point. The aim of this paper is to extend this analytic normalization…
We study the convergence of the Hermite series of measurable functions on the real line. We characterize the norm convergence of truncated partial Hermite sums in rearrangement invariant spaces provided that the truncations vanish…
Let $\mathcal A = \{A_{ij} \}_{i, j \in \mathcal I}$, where $\mathcal I$ is an index set, be a doubly indexed family of matrices, where $A_{ij}$ is $n_i \times n_j$. For each $i \in \mathcal I$, let $\mathcal V_i$ be an $n_i$-dimensional…
In this article we study the tropicalization of the Hilbert scheme and its suitability as a parameter space for tropical varieties. We prove that the points of the tropicalization of the Hilbert scheme have a tropical variety naturally…
A new renormalization scheme for theories with nontrivial internal symmetry is proposed. The scheme is regularization independent and respects the symmetry requirements.