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The space of Bridgeland stability conditions on the bounded derived category of coherent sheaves on P2 has a principle connected component Stab^\dag(P2). We show that Stab^\dag(P2) is the union of geometric and algebraic stability…

Algebraic Geometry · Mathematics 2016-11-08 Chunyi Li

Consider a 2-Calabi--Yau triangulated category with a Bridgeland stability condition. We devise an effective procedure to reduce the phase spread of an object by applying spherical twists. Using this, we give new proofs of the following…

Representation Theory · Mathematics 2021-08-23 Asilata Bapat , Anand Deopurkar , Anthony M. Licata

We present a novel notion of stable objects in a triangulated category. This Postnikov-stability is preserved by equivalences. We show that for the derived category of a projective variety this notion includes the case of semistable…

Algebraic Geometry · Mathematics 2009-01-13 Georg Hein , David Ploog

We show that, under mild conditions, the space of numerical Bridgeland stability conditions Stab(T) on a triangulated category T is complete. In particular the metric on a full component of Stab(T) for which the central charges factor…

Algebraic Geometry · Mathematics 2014-02-26 Jon Woolf

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 prove that moduli spaces of meromorphic quadratic differentials with simple zeroes on compact Riemann surfaces can be identified with spaces of stability conditions on a class of CY3 triangulated categories defined using quivers with…

Algebraic Geometry · Mathematics 2014-09-05 Tom Bridgeland , Ivan Smith

On a smooth projective threefold, we show that there are only two isomorphism types for the moduli of stable objects with respect to Bayer's standard polynomial Bridgeland stability - the moduli of Gieseker-stable sheaves and the moduli of…

Algebraic Geometry · Mathematics 2012-08-02 Jason Lo

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

Let $(X,H)$ be a smooth, projective, polarized surface over $\mathbb{C}$, and let $v \in K_{\mathrm{num}}(X)$ be a class of positive rank. We prove that for certain Bridgeland stability conditions $\sigma = (\mathcal{A}, Z)$ "on the…

Algebraic Geometry · Mathematics 2020-07-27 Tuomas Tajakka

We construct a family of non-geometric Bridgeland stability conditions on certain wrapped Fukaya categories, using homological mirror symmetry and categorical K\"unneth formulae. These stability conditions correspond to certain holomorphic…

Symplectic Geometry · Mathematics 2026-03-23 Yu-Wei Fan

We study stability conditions induced by functors between triangulated categories. Given a finite group acting on a smooth projective variety we prove that the subset of invariant stability conditions embeds as a closed submanifold into the…

Algebraic Geometry · Mathematics 2009-01-10 Emanuele Macri , Sukhendu Mehrotra , Paolo Stellari

We study projectivity of moduli spaces on the DT/PT wall crossing in Bridgeland and polynomial stability on a smooth, projective threefold. First, we construct a globally generated line bundle on the moduli stack of higher-rank…

Algebraic Geometry · Mathematics 2026-04-03 Mihai Pavel , Tuomas Tajakka

This paper gives a description of the full space of Bridgeland stability conditions on the bounded derived category of a contraction algebra associated to a 3-fold flop. The main result is that the stability manifold is the universal cover…

Algebraic Geometry · Mathematics 2022-08-02 Jenny August , Michael Wemyss

We propose the notion of stability on a triangulated category that is a generalization of the T.Bridgeland's stability data. We establish connections between stabilities and t-structures on a category and as application we get the…

Algebraic Geometry · Mathematics 2007-05-23 A. Gorodentscev , S. Kuleshov , A. Rudakov

We develop a unified approach for identifying spaces of stability conditions of triangulated categories arising from weighted marked surfaces with moduli spaces of quadratic differentials. This approach is based on the notion of a perverse…

Representation Theory · Mathematics 2024-06-26 Merlin Christ , Fabian Haiden , Yu Qiu

We give another proof of Le Potier's result and some variants on moduli spaces of semistable sheaves on the projective plane, using the Bridgeland stability conditions. As an application we study the wall-crossing phenomena of the Hilbert…

Algebraic Geometry · Mathematics 2010-03-30 Ryo Ohkawa

We study Bridgeland moduli spaces of semistable objects of $(-1)$-classes and $(-4)$-classes in the Kuznetsov components on index one prime Fano threefold $X_{4d+2}$ of degree $4d+2$ and index two prime Fano threefold $Y_d$ of degree $d$…

Algebraic Geometry · Mathematics 2021-07-13 Zhiyu Liu , Shizhuo Zhang

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

We give a structure result on the set of locally constant stability conditions, $\operatorname{Stab}(\mathcal{D}/R)$, defined by Halpern-Leistner-Robotis showing that it has the structure of a complex manifold, in total analogy with…

Algebraic Geometry · Mathematics 2026-04-01 Ian Selvaggi

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