Related papers: Nash multiplicities and resolution invariants
We first present the mixed Hilbert-Samuel multiplicities of analytic local rings over \mathbb{C} as generalized Lelong numbers and further represent them as intersection numbers in the context of modifications. As applications, we give…
This paper deals with the Nash problem, which consists in proving that the number of families of arcs on a singular germ of a surface $S$ coincides with the number of irreducible components of the exceptional divisor in the minimal…
Let $(X,O)$ be a germ of a normal surface singularity, $\pi : \tilde X\longrightarrow X$ be the minimal resolution of singularities and let $A=(a_{i,j})$ be the $n\times n$ symmetrical intersection matrix of the exceptional set of $\tilde…
Let (X,0) be a germ of complex analytic normal variety, non-singular outside 0. An essential divisor over (X,0) is a divisorial valuation of the field of meromorphic functions on (X,0), whose center on any resolution of the germ is an…
In this paper we show that iterating Nash blowups or normalized Nash blowups does not resolve the singularities of algebraic varieties of dimension four or higher over an algebraically closed field of arbitrary characteristic.
The multiplicity of an algebraic curve $C$ in the complex plane at a point $p$ on that curve is defined as the number of points that occur at the intersection of $C$ with a general complex line that passes close to the point $p$. It is…
Approximation of real analytic functions by Nash functions is a classical topic in real geometry. In this paper, we focus on the Nash approximation of an analytic desingularization of a Nash function germ obtained by a sequence of…
In this paper we show that iterating (non-normalized) Nash blowups does not necessarily resolve the singularities of algebraic varieties of dimension three over fields of characteristic zero.
The Nash problem on arcs for normal surface singularities states that there are as many arc families on a germ (S,O) of a singular surface as there are essential divisors over (S,O). It is known that this problem can be reduced to the study…
In this paper we investigate the relation betwen the Nash modification and the Bi-Lipschtiz equivalent germs in the cases of two germs and for a family of hypersurfaces with isolated singularities.
We survey the proof of the Nash conjecture for surfaces and show how geometric and topological ideas developed in previous articles by the authors influenced it. Later we summarize the main ideas in the higher dimensional statement and…
For a germ $(X,0) \subset (\mathbb{C}^n,0)$ of reduced, equidimensional complex analytic singularity its Nash modification can be constructed as an analytic subvariety $ Z \subset \mathbb{C}^n \times G(k,n)$. We give a characterization of…
We introduce a higher-order version of the tangent map of a morphism and find a matrix representation. We then apply this matrix to solve a conjecture by T. Yasuda regarding the semigroup of the higher Nash blowup of formal curves. We first…
We prove that, for the jet scheme of a singular hypersurface, the blowup of a certain jet-related module is not an isomorphism. In conjunction with recent developments in the theory of Nash blowups, our result holds over fields of arbitrary…
In this paper we present new proofs using real spectra of the finiteness theorem on Nash trivial simultaneous resolution and the finiteness theorem on Blow-Nash triviality for isolated real algebraic singularities. That is, we prove that a…
A multiplication on persistence diagrams is introduced by means of Schubert calculus. The key observation behind this multiplication comes from the fact that the representation space of persistence modules has the structure of the Schubert…
The paper surveys several results on the topology of the space of arcs of an algebraic variety and the Nash problem on the arc structure of singularities.
We introduce anchored versions of the Nash inequality. They allow to control the $L^2$ norm of a function by Dirichlet forms that are not uniformly elliptic. We then use them to provide heat kernel upper bounds for diffusions in degenerate…
We solve the equivariant generalized Nash problem for any non-rational normal variety with torus action of complexity one. Namely, we give an explicit combinatorial description of the Nash order on the set of equivariant divisorial…
We characterize the convergence properties of traditional best-response (BR) algorithms in computing solutions to mixed-integer Nash equilibrium problems (MI-NEPs) that turn into a class of monotone Nash equilibrium problems (NEPs) once…