scholarly journals Bridgeland stability conditions on wild Kronecker quivers

2019 ◽  
Vol 352 ◽  
pp. 27-55 ◽  
Author(s):  
George Dimitrov ◽  
Ludmil Katzarkov
Keyword(s):  
Stability Conditions ◽  
Bridgeland Stability Conditions

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

scholarly journals A short proof of the deformation property of Bridgeland stability conditions

2019 ◽  
Vol 375 (3-4) ◽  
pp. 1597-1613
Author(s):  
Arend Bayer
Keyword(s):  
Stability Condition ◽  
Deformation Property ◽  
Short Proof ◽  
Central Charge ◽  
Direct Proof ◽  
Small Deformation ◽  
Stability Conditions ◽  
Effective Version ◽  
Bridgeland Stability Conditions ◽  
The Stability

Abstract The key result in the theory of Bridgeland stability conditions is the property that they form a complex manifold. This comes from the fact that given any small deformation of the central charge, there is a unique way to correspondingly deform the stability condition. We give a short direct proof of an effective version of this deformation property.

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.

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