相关论文: Nash problem for stable toric varieties

This paper shows the affirmative answer to the local Nash problem for a toric singularity and analytically pretoric singularity. As a corollary we obtain the affirmative answer to the local Nash problem for a quasi-ordinary singularity.

We revisit the problem of resolution of singularities of toric curves by iterating Nash modification. We give a bound on the number of iterations required to obtain the resolution. We also introduce a different approach on counting…

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…

It is a long-standing question whether an arbitrary variety is desingularized by finitely many normalized Nash blow-ups. We consider this question in the case of a toric variety. We interpret the normalized Nash blow-up in polyhedral terms,…

In this paper we describe the implementation that led to the counterexamples to the Nash blowup conjectures recently discovered by the authors. We also provide new examples of toric varieties with prescribed singularities that are not…

The Nash problem on arc families is affirmatively answered for a toric variety by Ishii and Kollar's paper which also shows the negative answer for general case. The Nash problem is one of questions about the relation between arc families…

This paper studies Nash equilibrium problems that are given by polynomial functions. We formulate efficient polynomial optimization problems for computing Nash equilibria. The Lasserre type Moment-SOS relaxations are used to solve them.…

We investigate a modular convex Nash equilibrium problem involving nonsmooth functions acting on linear mixtures of strategies, as well as smooth coupling functions. An asynchronous block-iterative decomposition method is proposed to solve…

We prove an existence result for the time-dependent generalized Nash equilibrium problem under generalized convexity using a fixed point theorem. Furthermore, an application to the dynamic abstract economy is considered.

This paper studies the Nash stability in hedonic coalition formation games. We address the following issue: for a general problem formulation, is there any utility allocation method ensuring a Nash-stable partition? We propose the…

We give an affirmative answer to Nash Problem for quotient surface singularities, in particular for the icosahedral singularity $E_8$.

This paper gives out the solution of divergent Navier-Stokes equations, and shows that in this case, under a physicalacceptable condition, the solution would be smooth .

In this note we collect some results on the deformation theory of toric Fano varieties.

In this paper we prove that for toric varieties the uniform K-stability is the necessary condition for the existence of extremal metrics.

It has been recently shown that the iteration of Nash modification on not necessarily normal toric varieties corresponds to a purely combinatorial algorithm on the generators of the semigroup associated to the toric variety. We will show…

In this paper we introduce a maximal divisorial set in the arc space of a variety. The generalized Nash problem is reduced to a translation problem of the inclusion of two maximal divisorial sets. We study this problem and show a counter…

We propose a generalization of the classical stable marriage problem. In our model, the preferences on one side of the partition are given in terms of arbitrary binary relations, which need not be transitive nor acyclic. This generalization…

In this paper, the large time behavior of solutions of 1-D isentropic Navier-Stokes system is investigated. It is shown that a composite wave consisting of two viscous shock waves is stable for the Cauchy problem provided that the two waves…

We present a complete classification of normal toric surfaces that are resolved by a single normalized Nash blowup. Likewise, we obtain a complete classification of those resolved by a single Nash blowup. In both cases, the classification…

We prove weak-strong uniqueness results for the isentropic compressible Navier-Stokes system on the torus. In other words, we give conditions on a strong solution so that it is unique in a class of weak solutions. Known weak-strong…