Related papers: Extension Theorems for differential forms on low-d…

Let $(R,\mathfrak{m},\mathbb{k})$ be an equicharacteristic one-dimensional complete local domain over an algebraically closed field $\mathbb{k}$ of characteristic 0. R. Berger conjectured that R is regular if and only if the universally…

In this paper we give a new and simple algorithm to put any multivariate polynomial into a normal determinant form in which each entry has the form , and in each column the same variable appears. We also apply the algorithm to obtain a…

We study the pullback of the stable and augmented base locus under a finite surjective morphism between normal varieties over a perfect field.

We construct a continuous Lagrangian, strictly convex and superlinear in the third variable, such that the associated variational problem has a Lipschitz minimizer which is non-differentiable on a dense set. More precisely, the upper and…

In natural characteristic, smooth induction from an open subgroup does not always give an exact functor. In this article we initiate a study of the right derived functors, and we give applications to the non-existence of projective…

We show that a four-dimensional complete gradient shrinking Ricci soliton with positive isotropic curvature is either a quotient of S^4 or a quotient of S^3 cross R. This gives a clean classification result removing the earlier additional…

In this paper we show that the real differential of any injective slice regular function is everywhere invertible. The result is a generalization of a theorem proved by G. Gentili, S. Salamon and C. Stoppato, and it is obtained thanks, in…

This paper is devoted to the study of a newly introduced tool, projectional coderivatives and the corresponding calculus rules in finite dimensions. We show that when the restricted set has some nice properties, more specifically, is a…

In this paper we study quotients of Lie algebroids and groupoids endowed with compatible differential forms. We identify Lie theoretic conditions under which such forms become basic and characterize the induced forms on the quotients. We…

On a bounded three-dimensional smooth domain, we consider the generalized oscillon equation with Dirichlet boundary conditions, with time-dependent damping and time-dependent squared speed of propagation. Under structural assumptions on the…

Let $\Bbbk$ be an algebraically closed field of characteristic $p>2$. Let $\mathcal{O}_n=\Bbbk[X_1,\ldots,X_n]/(X_1^p,\ldots, X_n^p)$, a truncated polynomial ring in $n$ variables, and denote by $\mathcal{L}$ the derivation algebra of…

We introduce the foliated anti-self dual equation for higher dimensional smooth manifolds with codimension-4 Riemannian foliations. Several fundamental results are established, towards the defining of a Donaldson type invariant for such…

We show that a strong well-based cylindrical algebraic decomposition P of a bounded semi-algebraic set is a regular cell decomposition, in any dimension and independently of the method by which P is constructed. Being well-based is a global…

This paper aims to establish counterparts of fundamental regularity statements for solutions to elliptic equations in the setting of low-dimensional structures such as, for instance, glued manifolds or CW-complexes. The main result proves…

This is a short survey on the connection between general extension theories and the study of realizations of elliptic operators A on smooth domains in R^n, n > 1. The theory of pseudodifferential boundary problems has turned out to be very…

In this paper, we completely classify $3$-dimensional complete self-expanders with constant norm $S$ of the second fundamental form and constant $f_{3}$ in Euclidean space $\mathbb R^{4}$, where $h_{ij}$ are components of the second…

We extend Orlov's result that certain functors between derived categories of smooth projective varieties are Fourier--Mukai transforms to the case when those varieties are smooth and proper.

Imposing a strong condition on the linear order of shellable complexes, we introduce strong shellability. Basic properties, including the existence of dimension-decreasing strong shelling orders, are developed with respect to nonpure…

We prove that function fields of varieties of dimension at least two over an algebraic closure of a finite field are determined, modulo purely inseparable extensions, by the quotient by the second term in the lower central series of their…

This work explores the space of foliations on projective spaces over algebraically closed fields of positive characteristic, with a particular focus on the codimension one case. It describes how the irreducible components of these spaces…