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Related papers: Bridgeland stability conditions on normal surfaces

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We introduce the notion of a polynomial stability condition, generalizing Bridgeland stability conditions on triangulated categories. We construct and study a family of polynomial stability conditions for any normal projective variety. This…

Algebraic Geometry · Mathematics 2014-11-11 Arend Bayer

Let $\mathcal{T}$ be a $k$-linear triangulated category. The space of Bridgeland stability conditions on $\mathcal{T}$, denoted by $\mathrm{Stab}(\mathcal{T})$, forms a complex manifold. In this paper, we introduce an equivalence relation…

Algebraic Geometry · Mathematics 2025-06-30 Chunyi Li

We present a generalization of the Bogomolov-Miyaoka-Yau inequality to Deligne-Mumford surfaces of general type.

Algebraic Geometry · Mathematics 2020-08-27 Jiun-Cheng Chen , Hsian-Hua Tseng

In this paper we examine the conditions that an object $E$ with $\text{ch}_0(E)=0$ has to satisfy in order for it to be asymptotically (semi)stable with regard to Weak or Bridgeland stability conditions. This notion turned out to be…

Algebraic Geometry · Mathematics 2021-04-20 Victor Pretti

We study Bridgeland stability conditions on smooth surfaces arising from birational morphisms $S \to T$ to a singular surface. Assuming that $T$ has only ADE singularities or certain cyclic quotient singularities, we produce pre-stability…

Algebraic Geometry · Mathematics 2025-08-12 Nicolás Vilches

In this paper, we give a definition of weak stability condition on a triangulated category. The difference between our definition and existing definitions is that we allow objects in the kernel to have non-maximal phases. We then construct…

Algebraic Geometry · Mathematics 2024-10-04 Tristan C. Colllins , Jason Lo , Yun Shi , Shing-Tung Yau

We define and study a gluing procedure for Bridgeland stability conditions in the situation when a triangulated category has a semiorthogonal decomposition. As an application we construct stability conditions on the derived categories of…

Algebraic Geometry · Mathematics 2010-05-17 John Collins , Alexander Polishchuk

Let $S$ be a smooth projective surface on a smooth threefold $X$ such that $X$ has Picard rank 1 and NS$(S)$ is generated by the restriction of divisors from X. We show that if $X$ satisfies the Bogomolov-Gieseker type inequality for tilt…

Algebraic Geometry · Mathematics 2019-09-17 Geoffrey Smith

The purpose of this note is to give a new proof of Alexeev's boundedness result for stable surfaces which is independent of the base field and to highlight some important consequences of this result.

Algebraic Geometry · Mathematics 2016-10-04 Christopher D. Hacon , Sándor J Kovács

In this work stability of polygonal configurations on a plane and sphere is investigated. The conditions of linear stability are obtained. A nonlinear analysis of the problem is made with the help of Birkhoff normalization. Some problems…

Chaotic Dynamics · Physics 2007-05-23 A. V. Borisov , A. A. Kilin

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…

Category Theory · Mathematics 2014-10-06 George Dimitrov , Ludmil Katzarkov

We construct a subset of the space of stability conditions for any projective threefold with an ample polarization that satisfies a certain Bogomolov-Gieseker inequality to refine the result in arXiv:1410.1585. Then, we demonstrate that the…

Algebraic Geometry · Mathematics 2024-08-02 Dongjian Wu , Nantao Zhang

We consider a thin and narrow rectangular plate where the two short edges are hinged whereas the two long edges are free. This plate aims to represent the deck of a bridge, either a footbridge or a suspension bridge. We study a nonlocal…

Analysis of PDEs · Mathematics 2016-08-26 Vanderley Ferreira , Filippo Gazzola , Ederson Moreira dos Santos

In this article, we treat stability conditions in the sense of King, Bridgeland and Bayer in a single framework. Following King, we begin with weight functions on a triangulated category, and consider increasingly specialised configurations…

Algebraic Geometry · Mathematics 2021-03-18 Jason Lo

Let $X$ be a smooth projective threefold of Picard number one for which the generalized Bogomlov-Gieseker inequality holds. We characterize the limit Bridgeland semistable objects at large volume in the vertical region of the geometric…

Algebraic Geometry · Mathematics 2021-12-03 Marcos Jardim , Antony Maciocia , Cristian Martinez

We introduce the notions of categorical systoles and categorical volumes of Bridgeland stability conditions on triangulated categories. We prove that for any projective K3 surface, there exists a constant C depending only on the rank and…

Algebraic Geometry · Mathematics 2023-05-30 Yu-Wei Fan

In this paper, we study the action of an autoequivalence, the spherical twist associated to a torsion sheaf, on the standard Bridgeland stability conditions and a generalized weak stability condition on the derived category of a K3 surface.…

Algebraic Geometry · Mathematics 2025-10-27 Tristan C. Collins , Jason Lo , Yun Shi , Shing-Tung Yau

We realize explicit symmetries of Bridgeland stability conditions on any abelian threefold given by Fourier-Mukai transforms. In particular, we extend the previous joint work with Maciocia to study the slope and tilt stabilities of sheaves…

Algebraic Geometry · Mathematics 2017-09-28 Dulip Piyaratne

For a smooth projective complex variety whose Albanese morphism is finite, we show that every Bridgeland stability condition on its bounded derived category of coherent sheaves is geometric, in the sense that all skyscraper sheaves are…

Algebraic Geometry · Mathematics 2022-01-24 Lie Fu , Chunyi Li , Xiaolei Zhao

On a given arithmetic surface, inspired by work of Miyaoka, we consider vector bundles which are extensions of a line bundle by another one. We give sufficient conditions for their restriction to the generic fiber to be semi-stable. We then…

Algebraic Geometry · Mathematics 2007-05-23 C. Soule