Related papers: Stability Manifold of P^1

We give a new proof of homological stability with the best known isomorphism range for mapping class groups of surfaces with respect to genus. The proof uses the framework of Randal-Williams-Wahl and Krannich applied to disk stabilization…

We construct stable manifolds for a class of degenerate evolution equations including the steady Boltzmann equation, establishing in the process exponential decay of associated kinetic shock and boundary layers to their limiting equilibrium…

We prove the Bogomolov-Gieseker type inequality conjectured by Bayer, Macri and Toda for some products of three curves. This gives the first examples of Bridgeland stability conditions on some threefolds of general type. The key ingredients…

In these lecture notes we give an introduction to Bridgeland stability conditions on smooth complex projective varieties with a particular focus on the case of surfaces. This includes basic definitions of stability conditions on derived…

In the present paper we discuss stability of the tanget bundle of a Fano n-fold of index >= n-2 and b_2=1. For example, we prove that all Fano 4-folds with b_2=1 have stable tangent bundle. For this purpose we prove some vanishing theorems…

A group may be considered $C^*$-stable if almost representations of the group in a $C^*$-algebra are always close to actual representations. We initiate a systematic study of which discrete groups are $C^*$-stable or only stable with…

Using results in a previous paper "Non-semistable exceptional objects in hereditary categories", we focus here on studying the topology of the space of Bridgeland stability conditions on $D^b(Rep_k(Q ))$, where $Q$ is the acyclic triangular…

We give a criterion for slope-stability of the syzygy bundle of a globally generated ample line bundle on a smooth projective variety of Picard number $1$ in terms of Hilbert polynomial. As applications, we prove the stability of syzygy…

We study some wrapped configurations of branes in the near-horizon geometry of a stack of other branes. The common feature of all the cases analyzed is a quantization rule and the appearance of a finite number of static configurations in…

It was recently suggested by A. Kapustin that turning on a $B$-field, and allowing some discrepancy between the left and and right-moving complex structures, must induce an identification of B-branes with holomorphic line bundles on a…

Let $X$ be a smooth compact complex surface with the canonical divisor $K_X$ ample and let $\Theta_X$ be its holomorphic tangent bundle. Bridgeland stability conditions are used to study the space $H^1 (\Theta_X)$ of infinitesimal…

Learning stable dynamical systems from data is crucial for safe and reliable robot motion planning and control. However, extending stability guarantees to trajectories defined on Riemannian manifolds poses significant challenges due to the…

In this paper, we study geometric rigidity of Riemannian manifolds admitting stable solutions of certain elliptic problems (stability in a variational sense), that is, under suitable hypotheses, we are able to characterize the Riemannian…

We construct Bridgeland stability conditions on the the following hyper-K\"ahler or strict Calabi--Yau manifolds: - Generalized Kummer varieties associated to an abelian surface that is isogenous to a product of elliptic curves. - Universal…

We formulate a notion of K-stability for K\"ahler manifolds, and prove one direction of the Yau-Tian-Donaldson conjecture in this setting. More precisely, we prove that the Mabuchi functional being bounded below (resp. coercive) implies…

We give new sufficient conditions for the integrability and unique integrability of continuous tangent sub-bundles on manifolds of arbitrary dimension, generalizing Frobenius' classical Theorem for C^1 sub-bundles. Using these conditions we…

We consider stable manifolds of a holomorphic diffeomorphism of a complex manifold. Using a conjugation of the dynamics to a (non-stationary) polynomial normal form, we show that typical stable manifolds are biholomorphic to complex…

We describe the relationship between two spaces associated to a quiver with potential. The first is a complex manifold parametrizing Bridgeland stability conditions on a triangulated category, and the second is a cluster variety with a…

We consider two classes of backgrounds of Type IIB supergravity obtained by wrapping D5-branes on a two-cycle inside the conifold. The field theory dual exhibits confinement and, in addition, a region in which the dynamics is walking, at…

The stability of Yang-Mills bundles over the usual $S^4$ space-time manifold is investigated according to the topological methods. The necessary gauge- and topological invaraint criterion for the exsitence of the related critical points is…