Related papers: Stable envelopes for critical loci

A convex envelope for the problem of finding the best approximation to a given matrix with a prescribed rank is constructed. This convex envelope allows the usage of traditional optimization techniques when additional constraints are added…

In this article, we establish a Hitchin-Kobayashi type correspondence for generalised Seiberg-Witten monopole equations on Kahler surfaces. We show that the "stability" criterion we obtain, for the existence of solutions, coincides with…

Given a quiver with potential $(Q,W)$, Kontsevich-Soibelman constructed a Hall algebra on the cohomology of the stack of representations of $(Q,W)$. As shown by Davison-Meinhardt, this algebra comes with a filtration whose associated graded…

We study quiver gauge theories on the round and squashed seven-spheres, and orbifolds thereof. They arise by imposing $G$-equivariance on the homogeneous space $G/H=\mathrm{SU}(4)/\mathrm{SU}(3)$ endowed with its Sasaki-Einstein structure,…

We use the Le Bruyn--Procesi theorem to prove several results on quiver schemes for nongeneric stability conditions: We show that the stability-zero finite-type Nakajima quiver schemes are reduced points and give an example of a closely…

We consider cohomological stable envelopes for a natural torus action $\mathsf{T}$ on $X=T^*Gr(k,n)$, introduced by Maulik-Okounkov. We define the $\mathbb{C}^*_\hbar$-equivariant integral of the stable envelope using equivariant…

Holomorphic chains on a Riemann surface arise naturally as fixed points of the natural C*-action on the moduli space of Higgs bundles. In this paper we associate a new quiver bundle to the Hom-complex of two chains, and prove that stability…

Given a quiver with potential $(Q,W)$, Kontsevich-Soibelman constructed a Hall algebra on the critical cohomology of the stack of representations of $(Q,W)$. Special cases of this construction are related to work of Nakajima, Varagnolo,…

We use stable graphs to package the $\mathrm{NMSP}$ relations. Our tools are the $S$ matrix of the $\mathcal{O}(5)$-twisted $ \mathbb P^{\mathrm N+4}$ equivariant GW theory, and the $R$ matrix obtained from the stablization of the theory's…

Consider a finite-dimensional real vector space equipped with a finite group acting unitarily on it. We address the general problem of constructing Euclidean stable embeddings of the quotient space of orbits. Our approach is based on…

In this paper we pose and prove a spacetime version of Gromov's dihedral rigidity theorem (Gromov, Li) for cubes when the dimension is 3 by studying the level sets of spacetime harmonic functions (Stern, Bray-Stern, Hirsch-Kazaras-Khuri),…

In this paper, we consider how the approach of Bezrukavnikov and Kaledin to understanding the categories of coherent sheaves on symplectic resolutions can be applied to the Coulomb branches introduced by Braverman, Finkelberg and Nakajima.…

We define and compute higher rank analogs of Pandharipande-Thomas stable pair invariants in primitive classes for K3 surfaces. Higher rank stable pair invariants for Calabi-Yau threefolds have been defined by Sheshmani \cite{shesh1,shesh2}…

We study corotational wave maps from $(1+3)$-dimensional Minkowski space into the three-sphere. We establish the asymptotic stability of an explicitly known self-similar wave map under perturbations that are small in the critical Sobolev…

The goal of the paper is to introduce a version of Schubert calculus for each dihedral reflection group W. That is, to each "sufficiently rich'' spherical building Y of type W we associate a certain cohomology theory and verify that, first,…

We consider the cotangent bundle $T^*F_\lambda$ of a $GL_n$ partial flag variety, $\lambda=(\lambda_1,...,\lambda_N)$, $|\lambda|=\sum_i\lambda_i=n$, and the torus $T=(\C^\times)^{n+1}$ equivariant K-theory algebra $K_T(T^*F_\lambda)$. We…

For a finite subgroup $\Gamma\subset \mathrm{SL}(2,\mathbb{C})$ and $n\geq 1$, we construct the (reduced scheme underlying the) Hilbert scheme of $n$ points on the Kleinian singularity $\mathbb{C}^2/\Gamma$ as a Nakajima quiver variety for…

For a finite subgroup $\Gamma\subset {\mathrm{SL}}(2,\mathbb{C})$, we identify fine moduli spaces of certain cornered quiver algebras, defined in earlier work, with orbifold Quot schemes for the Kleinian orbifold $[\mathbb{C}^2/\Gamma]$. We…

The equivariant Chern-Schwartz-MacPherson (CSM) class and the equivariant Motivic Chern (MC) class are important characteristic classes of singular varieties in cohomology and K theory---and their theory overlaps with the theory of…

We expose in detail the principle that the relative geometric invariant theory of equivariant morphisms is related to the GIT for linearizations near the boundary of the $G$-effective ample cone. We then apply this principle to construct…