Related papers: A one-step counterexample to the normalized Nash b…

Any toric flip naturally induces an equivalence between the associated categories of equivariant reflexive sheaves, and we investigate how slope stability behaves through this functor. On one hand, for a fixed toric sheaf, and natural…

The subject is partial resolution of singularities. Given an algebraic variety X (not necessarily equidimensional) in characteristic zero (or, more generally, a pair (X,D), where D is a divisor on X), we construct a functorial…

Let X be an analytic vector field defined in a real analytic manifold of dimension three. We prove that all the singularities of X can be made elementary by a finite number of blowing-ups in the ambient space. New version: Some misprints…

We describe a class of toric varieties in the $N$-dimensional affine space which are minimally defined by no less than $N-2$ binomial equations.

We show that Fourier transforms on the Weyl algebras have a geometric counterpart in the framework of toric varieties, namely they induce isomorphisms between twisted rings of differential operators on regular toric varieties, whose fans…

We prove that if $(X,A+B)$ is a pair defined over an algebraically closed field of positive characteristic such that $(X,B)$ is strongly $F$-regular, $A$ is ample and $K_X+A+B$ is strictly nef, then $K_X+A+B$ is ample. Similarly, we prove…

For a smooth finite cyclic covering over a projective space of dimension greater than one, we show that the group of automorphisms acts faithfully on the cohomology except for a few cases. In characteristic zero, we study the equivariant…

Counterfactual explanations describe how to modify a feature vector in order to flip the outcome of a trained classifier. Obtaining robust counterfactual explanations is essential to provide valid algorithmic recourse and meaningful…

We combine several folklore observations to provide a working framework for iterating constructions which contradict the axiom of choice. We use this to define a model in which any kind of structural failure must fail with a proper class of…

The goal of this study is to investigate the local convergence of a three-step Newton-Traub technique for solving nonlinear equations in Banach spaces with a convergence rate of five. The first order derivative of a nonlinear operator is…

Enhanced ind-sheaves provide a suitable framework for the irregular Riemann-Hilbert correspondence. In this paper, we give some precisions on nearby and vanishing cycles for enhanced perverse objects in dimension one. As an application, we…

We show how to extend Epstein's algebraic transversality principles for rational maps $f$ of ${\mathbb P}^1_{\mathbb C}$ to infinite forward invariant subsets of the Fatou set. The key, at least conceptually, to doing this is to have a…

We explain that the logic behind the derivation of the Noumi-Shiraishi function can be applied directly to the Baker-Akhiezer function (BAF). This amounts to changing an ansatz for BAF to a nested one, where the BAF of N + 1 variables is…

For $(n+1)$-webs by curves in an ambiant $n$-dimensional manifold, we first define a generalization of the well known Blaschke curvature of the dimension two, which vanishes iff the web has the maximum possible rank which is one. But,…

We introduce the notion of a \emph{conic sequence} of a convex polytope. It is a way of building up a polytope starting from a vertex and attaching faces one by one with certain regulations. We apply this to a toric variety to obtain an…

An elementary, at the undergraduate level derivation is given of precise upper bounds of the number of various RNA secondary structures. The method works when the generating function has multiple singularities at the circle of convergence,…

We prove that if an $n$-dimensional space $X$ satisfies certain topological conditions then any triangulation of $X$ as well as any its representation as a simplicial set with contractible faces has at least $2^n$ faces of dimension $n$.…

We study exceptional loci of F-blowups of normal toric varieties. In the $\Q$-factorial case, this study amounts to studying the exceptional loci of $G$-Hilbert schemes. We give a formula for the dimension of the center of a prime divisor…

A strong version of a conjecture of Viterbo asserts that all normalized symplectic capacities agree on convex domains. We review known results showing that certain specific normalized symplectic capacities agree on convex domains. We also…

We propose and study a generalized version of the Lipman-Zariski conjecture: let $(x \in X)$ be an $n$-dimensional singularity such that for some integer $1 \le p \le n - 1$, the sheaf $\Omega_X^{[p]}$ of reflexive differential $p$-forms is…