scholarly journals Polynomial Bridgeland stability conditions for the derived category of sheaves on surfaces

2011 ◽  
Vol 19 (1) ◽  
pp. 31-52
Author(s):  
Wei-Ping Li ◽  
Zhenbo Qin
Keyword(s):  
Derived Category ◽  
Stability Conditions ◽  
Bridgeland Stability Conditions

scholarly journals Contractibility of the stability manifold for silting-discrete algebras

2018 ◽  
Vol 30 (5) ◽  
pp. 1255-1263 ◽  
Author(s):  
David Pauksztello ◽  
Manuel Saorín ◽  
Alexandra Zvonareva
Keyword(s):  
Derived Category ◽  
Stability Conditions ◽  
Bridgeland Stability Conditions ◽  
The Stability ◽  
Stability Manifold

AbstractWe show that any bounded t-structure in the bounded derived category of a silting-discrete algebra is algebraic, i.e. has a length heart with finitely many simple objects. As a corollary, we obtain that the space of Bridgeland stability conditions for a silting-discrete algebra is contractible.

The wall-crossing behavior for Bridgeland’s stability conditions on abelian and K3 surfaces

2018 ◽  
Vol 2018 (735) ◽  
pp. 1-107 ◽  
Author(s):  
Hiroki Minamide ◽  
Shintarou Yanagida ◽  
Kōta Yoshioka
Keyword(s):  
Stability Condition ◽  
Derived Category ◽  
The Other ◽  
Abelian Surface ◽  
Stability Conditions ◽  
Abelian Surfaces ◽  
Coherent Sheaves ◽  
Fundamental Properties ◽  
Wall Crossing ◽  
Wall Crossing Formula

AbstractThe wall-crossing behavior for Bridgeland’s stability conditions on the derived category of coherent sheaves on K3 or abelian surface is studied. We introduce two types of walls. One is called the wall for categories, where thet-structure encoded by stability condition is changed. The other is the wall for stabilities, where stable objects with prescribed Mukai vector may get destabilized. Some fundamental properties of walls and chambers are studied, including the behavior under Fourier–Mukai transforms. A wall-crossing formula of the counting of stable objects will also be derived. As an application, we will explain previous results on the birational maps induced by Fourier–Mukai transforms on abelian surfaces. These transformations turns out to coincide with crossing walls of certain property.

scholarly journals Fourier–Mukai transforms and Bridgeland stability conditions on abelian threefolds II

2016 ◽  
Vol 27 (01) ◽  
pp. 1650007 ◽  
Author(s):  
Antony Maciocia ◽  
Dulip Piyaratne
Keyword(s):  
Type Inequality ◽  
Stability Conditions ◽  
Coherent Sheaves ◽  
Rank One ◽  
Bridgeland Stability Conditions ◽  
Abelian Categories

We show that the conjectural construction proposed by Bayer, Bertram, Macrí and Toda gives rise to Bridgeland stability conditions for a principally polarized abelian threefold with Picard rank one by proving that tilt stable objects satisfy the strong Bogomolov–Gieseker (BG) type inequality. This is done by showing certain Fourier–Mukai transforms (FMTs) give equivalences of abelian categories which are double tilts of coherent sheaves.

scholarly journals Systolic inequalities for K3 surfaces via stability conditions

2021 ◽  
Author(s):  
Yu-Wei Fan
Keyword(s):  
Stability Condition ◽  
Symplectic Geometry ◽  
K3 Surfaces ◽  
Stability Conditions ◽  
Triangulated Categories ◽  
K3 Surface ◽  
Bridgeland Stability Conditions ◽  
Systolic Inequality

AbstractWe introduce the notions of categorical systoles and categorical volumes of Bridgeland stability conditions on triangulated categories. We prove that for any projective K3 surface X, there exists a constant C depending only on the rank and discriminant of NS(X), such that $$\begin{aligned} \mathrm {sys}(\sigma )^2\le C\cdot \mathrm {vol}(\sigma ) \end{aligned}$$ sys ( σ ) 2 ≤ C · vol ( σ ) holds for any stability condition on $$\mathcal {D}^b\mathrm {Coh}(X)$$ D b Coh ( X ) . This is an algebro-geometric generalization of a classical systolic inequality on two-tori. We also discuss applications of this inequality in symplectic geometry.

scholarly journals Weil–Petersson geometry on the space of Bridgeland stability conditions

2021 ◽  
Vol 29 (3) ◽  
pp. 681-706
Author(s):  
Yu-Wei Fan ◽  
Atsushi Kanazawa ◽  
Shing-Tung Yau
Keyword(s):  
Stability Conditions ◽  
Bridgeland Stability Conditions
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