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Related papers: Gluing stability conditions

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Recently, Anno, Bezrukavnikov and Mirkovic have introduced the notion of a "real variation of stability conditions" (which is related to Bridgeland's stability conditions), and construct an example using categories of coherent sheaves on…

Representation Theory · Mathematics 2015-12-25 Vinoth Nandakumar

We construct Bridgeland stability conditions on the derived category of smooth quasi-projective Deligne-Mumford surfaces whose coarse moduli spaces have ADE singularities. This unifies the construction for smooth surfaces and Bridgeland's…

Algebraic Geometry · Mathematics 2021-10-22 Bronson Lim , Franco Rota

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

Given a triangulated category $D$ with an action of a fusion category $C$, we study the moduli space $Stab_{C}(D)$ of fusion-equivariant Bridgeland stability conditions on $D$. The main theorem is that the fusion-equivariant stability…

Representation Theory · Mathematics 2025-08-05 Hannah Dell , Edmund Heng , Anthony M. Licata

Categorical resolutions of singularities are a replacement of resolution of singularities within the realm of triangulated categories. They allow the study of the derived category of a singular variety $X$ via a triangulated category that…

Algebraic Geometry · Mathematics 2025-12-05 Nicolás Vilches

This paper investigates the wall structure of the space of stability conditions on Hirzebruch surfaces. Using the gluing construction of \cite{CP} and \cite{Uch} with respect to a fixed semiorthogonal decomposition, we focus on two main…

Algebraic Geometry · Mathematics 2026-01-14 Yusuke Ohmiya

Using Bridgeland stability conditions we give sufficient criteria for a stable vector bundle on a surface to remain stable when restricted to a curve. We give a stronger criterion when the vector bundle is a general vector bundle on the…

Algebraic Geometry · Mathematics 2020-06-16 John Kopper

We consider a 3-Calabi-Yau triangulated category associated to an ideal triangulation of a marked bordered surface. Using the theory of harmonic maps between Riemann surfaces, we construct a natural map from a component of the space of…

Geometric Topology · Mathematics 2024-10-08 Dylan G. L. Allegretti

Stability conditions on triangulated categories were introduced by Bridgeland as a 'continuous' generalisation of t-structures. The set of locally-finite stability conditions on a triangulated category is a manifold which has been studied…

Representation Theory · Mathematics 2016-10-03 Peter Jorgensen , David Pauksztello

In this article, we show that some semi-rigid $\mu$-stable sheaves on a projective K3 surface $X$ with Picard number 1 are stable in the sense of Bridgeland's stability condition. As a consequence of our work, we show that the special set…

Algebraic Geometry · Mathematics 2011-05-18 Kotaro Kawatani

We propose compactifications of the moduli space of Bridgeland stability conditions of a triangulated category. Our construction arises from a viewing a stability condition as a metric on the underlying category and is inspired by the…

Representation Theory · Mathematics 2023-11-10 Asilata Bapat , Anand Deopurkar , Anthony M. Licata

We introduce a general method to induce Bridgeland stability conditions on semiorthogonal components of triangulated categories. In particular, we prove the existence of Bridgeland stability conditions on the Kuznetsov component of the…

Algebraic Geometry · Mathematics 2023-06-14 Arend Bayer , Martí Lahoz , Emanuele Macrì , Paolo Stellari

We develop a theory of Bridgeland stability conditions and moduli spaces of semistable objects for a family of varieties. Our approach is based on and generalizes previous work by Abramovich-Polishchuk, Kuznetsov, Lieblich, and…

Algebraic Geometry · Mathematics 2022-01-26 Arend Bayer , Martí Lahoz , Emanuele Macrì , Howard Nuer , Alexander Perry , Paolo Stellari

Let $X$ be a smooth projective variety over $\mathbb C$. In this paper, we prove that $\mathrm{D}^b(X)$, the bounded derived category of coherent sheaves on $X$, always admits stability conditions in the sense of Bridgeland.

Algebraic Geometry · Mathematics 2026-02-02 Chunyi Li

This paper contains a description of one connected component of the space of stability conditions on the bounded derived category of coherent sheaves on a complex algebraic K3 surface.

Algebraic Geometry · Mathematics 2007-05-23 Tom Bridgeland

I use Bridgeland's definition of a stability condition on a triangulated category to investigate the stability of D-branes on Calabi-Yau cones given by the canonical line bundle over a del Pezzo surface. In this context, I prove the…

High Energy Physics - Theory · Physics 2009-02-24 Aaron Bergman

We give a natural family of Bridgeland stability conditions on the derived category of a smooth projective complex surface S and describe ``wall-crossing behavior'' for objects with the same invariants as $\cO_C(H)$ when H generates Pic(S)…

Algebraic Geometry · Mathematics 2007-08-17 Daniele Arcara , Aaron Bertram , Max Lieblich

Let $R$ be a commutative ring. We introduce the notion of support of objects in an $R$-linear triangulated category. As an application, we study the non-existence of Bridgeland stability conditions on $R$-linear triangulated categories.

Algebraic Geometry · Mathematics 2023-01-11 Kotaro Kawatani

In this paper, we prove BG-type inequality conjecture for threefolds in the title. In particular, there exist Bridgeland stability conditions on these threefolds.

Algebraic Geometry · Mathematics 2020-07-28 Naoki Koseki

We give a explicit description of gluing stability conditions on ruled surfaces by introducing gluing perversity. Moreover, we describe a destabilizing wall of skyscraper sheaves on ruled surfaces by deformation of stability conditions…

Algebraic Geometry · Mathematics 2017-01-04 Takayuki Uchiba