Related papers: Higher Nash blowup on normal toric varieties

We are concerned with an elliptic problem which describes a mean field equation of the equilibrium turbulence of vortices with variable intensities. In the first part of the paper we describe the blow-up phenomenon and highlight the…

We study Gr\"obner degenerations of Schubert varieties inside flag varieties. We consider toric degenerations of flag varieties induced by matching fields and semi-standard Young tableaux. We describe an analogue of matching field ideals…

The paper deals with blow--up for the solutions of wave equation with nonlinear source and nonlinear boudary damping terms, posed in a bounded and regular domain. The initial data are posed in the energy space. The aim of the paper is to…

A natural higher K-theoretic analogue of the triviality of vector bundles on affine toric varieties is the conjecture on nilpotence of the multiplicative action of the natural numbers on the K-theory of these varieties. This includes both…

In a previous work with Tai-Peng Tsai, the author studied the dynamics of axisymmetric, swirl-free Euler equation in four and higher dimensions. One conclusion of this analysis is that the dynamics become dramatically more singular as the…

Let $H$ and $H'$ be two ample line bundles over a smooth projective surface $X$, and $M(H)$ (resp. $M(H')$) the coarse moduli scheme of $H$-semistable (resp. $H'$-semistable) sheaves of fixed type $(r,c_1,c_2)$. We construct a sequence of…

We study the normalized volume of toric singularities. As it turns out, there is a close relation to the notion of (non-symmetric) Mahler volume from convex geometry. This observation allows us to use standard tools from convex geometry,…

In this paper we describe the notion of a toric supervariety, generalizing that of a toric variety from the classical setting. We give a combinatorial interpretation of the category of quasinormal toric supervarieties with one odd dimension…

We study the greatest common divisor problem for torus invariant blowing-up morphisms of nonsingular toric Fano varieties. Our main result applies the theory of Okounkov bodies together with an arithmetic form of Cartan's Second Main…

We prove that the topological type of a normal surface singularity $(X,0)$ provides finite bounds for the multiplicity and polar multiplicity of $(X,0)$, as well as for the combinatorics of the families of generic hyperplane sections and of…

In this paper we perform a refined blow up analysis of finite energy approximated solutions to a Nirenberg type problem on half spheres. The later consists of prescribing, under minimal boundary conditions, the scalar curvature to be a…

In [19], the authors give minimal embedded toric resolutions of ADE-singularities in C^3 by constructing regular refinements of their dual Newton polyhedrons with the elements of their embedded valuation sets derived from the jet schemes…

We construct a functor from the category of manifolds with generalized corners to the category of complexes of toric monoids, and for every `refinement' of the complex associated to a manifold, we show there is a unique `blow-up', i.e., a…

The strong factorization conjecture states that a proper birational map between smooth algebraic varieties over a field of characteristic zero can be factored as a sequence of smooth blowups followed by a sequence of smooth blowdowns. We…

Let $G$ be a finite abelian subgroup of $PGL(r-1,K)=\mathrm{Aut}(\P^{r-1}_K)$. In this paper, we prove that the normalization of the $G$-orbit Hilbert scheme $\Hilb^G(\P^{r-1})$ is described as a toric variety, which corresponds to the…

We describe the structure of simplicial locally convex fans associated to even-dimensional complete toric varieties with signature 0. They belong to the set of such toric varieties whose even degree Betti numbers yield a top gamma vector…

We present an algebraic method to study four-dimensional toric varieties by lifting matrix equations from the special linear group ${\rm SL}_2({\mathbb Z})$ to its preimage in the universal cover of ${\rm SL}_2({\mathbb R})$. With this…

In this paper we show that a normal affine toric variety X different from the algebraic torus is uniquely determined by its automorphism group in the category of affine irreducible, not necessarily normal, algebraic varieties if and only if…

Heterotic orbifold models are promising candidates for models with MSSM like spectra. But orbifolds only correspond to a special place in moduli space, the bigger picture is described by the moduli space of Calabi-Yau spaces. In this talk…

Every real algebraic variety is isomorphic to the set of totally mixed Nash equilibria of some three-person game, and also to the set of totally mixed Nash equilibria of an $N$-person game in which each player has two pure strategies. From…