scholarly journals Computing the walls associated to Bridgeland stability conditions on projective surfaces

2014 ◽  
Vol 18 (2) ◽  
pp. 263-280 ◽  
Author(s):  
Antony Maciocia
Keyword(s):  
Stability Conditions ◽  
Bridgeland Stability Conditions ◽  
Projective Surfaces

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 Stability conditions and birational geometry of projective surfaces

2014 ◽  
Vol 150 (10) ◽  
pp. 1755-1788 ◽  
Author(s):  
Yukinobu Toda
Keyword(s):  
Moduli Spaces ◽  
Minimal Model ◽  
Derived Category ◽  
Stability Conditions ◽  
Birational Geometry ◽  
Projective Surface ◽  
Model Program ◽  
Minimal Model Program ◽  
Coherent Sheaves ◽  
Projective Surfaces

AbstractWe show that the minimal model program on any smooth projective surface is realized as a variation of the moduli spaces of Bridgeland stable objects in the derived category of coherent sheaves.

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.

Sign in / Sign up

Export Citation Format

Share Document