scholarly journals Donaldson–Thomas invariants of abelian threefolds and Bridgeland stability conditions

2021 ◽  
Vol 31 (1) ◽  
pp. 13-73
Author(s):  
Georg Oberdieck ◽  
Dulip Piyaratne ◽  
Yukinobu Toda
Keyword(s):  
Discriminant Function ◽  
Stability Conditions ◽  
Full Support ◽  
Wall Crossing ◽  
Rank One ◽  
Bridgeland Stability Conditions ◽  
Support Property ◽  
The Stability ◽  
Definition Of ◽  
Stability Manifold

We study the reduced Donaldson–Thomas theory of abelian threefolds using Bridgeland stability conditions. The main result is the invariance of the reduced Donaldson–Thomas invariants under all derived autoequivalences, up to explicitly given wall-crossing terms. We also present a numerical criterion for the absence of walls in terms of a discriminant function. For principally polarized abelian threefolds of Picard rank one, the wall-crossing contributions are discussed in detail. The discussion yields evidence for a conjectural formula for curve counting invariants by Bryan, Pandharipande, Yin, and the first author. For the proof we strengthen several known results on Bridgeland stability conditions of abelian threefolds. We show that certain previously constructed stability conditions satisfy the full support property. In particular, the stability manifold is non-empty. We also prove the existence of a Gieseker chamber and determine all wall-crossing contributions. A definition of reduced generalized Donaldson–Thomas invariants for arbitrary Calabi–Yau threefolds with abelian actions is given.

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.

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 ON THE STABILITY CONDITIONS OF 2D TIME FRACTIONAL DIFFUSION EQUATION

2020 ◽  
Vol 25 (1) ◽  
pp. 11-15 ◽  
Author(s):  
Adel Rashed A. Ali Alsabbagh ◽  
Esraa Abbas Al-taai
Keyword(s):  
Diffusion Equation ◽  
Time Derivative ◽  
Fractional Diffusion ◽  
Fractional Diffusion Equation ◽  
Stability Conditions ◽  
Two Dimensional ◽  
Time Fractional Diffusion Equation ◽  
The Stability ◽  
Definition Of ◽  
Good Agreement

The Caputo definition of fractional derivative has been employed for the time derivative for the two-dimensional time-fractional diffusion equation. The stability condition obtained by reformulation the classical multilevel technique on the finite difference scheme. A numerical example gives a good agreement with the theoretical result

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 Stability conditions for generic K3 categories

2008 ◽  
Vol 144 (1) ◽  
pp. 134-162 ◽  
Author(s):  
Daniel Huybrechts ◽  
Emanuele Macrì ◽  
Paolo Stellari
Keyword(s):  
K3 Surfaces ◽  
Derived Categories ◽  
Picard Group ◽  
Stability Conditions ◽  
Abelian Surfaces ◽  
Coherent Sheaves ◽  
The Stability ◽  
Stability Manifold

AbstractA K3 category is by definition a Calabi–Yau category of dimension two. Geometrically K3 categories occur as bounded derived categories of (twisted) coherent sheaves on K3 or abelian surfaces. A K3 category is generic if there are no spherical objects (or just one up to shift). We study stability conditions on K3 categories as introduced by Bridgeland and prove his conjecture about the topology of the stability manifold and the autoequivalences group for generic twisted projective K3, abelian surfaces, and K3 surfaces with trivial Picard group.

scholarly journals Mukai’s program (reconstructing a K3 surface from a curve) via wall-crossing

2020 ◽  
Vol 2020 (765) ◽  
pp. 101-137 ◽  
Author(s):  
Soheyla Feyzbakhsh
Keyword(s):  
Vector Bundles ◽  
Picard Group ◽  
Stability Conditions ◽  
K3 Surface ◽  
Wall Crossing ◽  
Bridgeland Stability Conditions ◽  
G 11

AbstractLet C be a curve of genus {g=11} or {g\geq 13} on a K3 surface whose Picard group is generated by the curve class {[C]}. We use wall-crossing with respect to Bridgeland stability conditions to generalise Mukai’s program to this situation: we show how to reconstruct the K3 surface containing the curve C as a Fourier–Mukai transform of a Brill–Noether locus of vector bundles on C.

scholarly journals Stability conditions in families

2021 ◽  
Author(s):  
Arend Bayer ◽  
Martí Lahoz ◽  
Emanuele Macrì ◽  
Howard Nuer ◽  
Alexander Perry ◽  
...  
Keyword(s):  
Infinite Series ◽  
Moduli Spaces ◽  
Stability Conditions ◽  
Hodge Conjecture ◽  
Semistable Reduction ◽  
The Family ◽  
Hyperkähler Manifolds ◽  
Bridgeland Stability Conditions ◽  
Support Property ◽  
Cubic Fourfold

AbstractWe 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 Piyaratne–Toda. Our notion includes openness of stability, semistable reduction, a support property uniformly across the family, and boundedness of semistable objects. We show that such a structure exists whenever stability conditions are known to exist on the fibers.Our main application is the generalization of Mukai’s theory for moduli spaces of semistable sheaves on K3 surfaces to moduli spaces of Bridgeland semistable objects in the Kuznetsov component associated to a cubic fourfold. This leads to the extension of theorems by Addington–Thomas and Huybrechts on the derived category of special cubic fourfolds, to a new proof of the integral Hodge conjecture, and to the construction of an infinite series of unirational locally complete families of polarized hyperkähler manifolds of K3 type.Other applications include the deformation-invariance of Donaldson–Thomas invariants counting Bridgeland stable objects on Calabi–Yau threefolds, and a method for constructing stability conditions on threefolds via degeneration.

Postmodern More

Moreana ◽  
2003 ◽  
Vol 40 (Number 153- (1-2) ◽  
pp. 219-239
Author(s):  
Anne Lake Prescott
Keyword(s):  
Human Language ◽  
Thomas More ◽  
The Stability ◽  
Definition Of ◽  
Recent Critic

Thomas More is often called a “humanist,” and rightly so if the word has its usual meaning in scholarship on the Renaissance. “Humanist” has by now acquired so many different and contradictory meanings, however, that it needs to be applied carefully to the likes of More. Many postmodernists tend to use the word, pejoratively, to mean someone who believes in an autonomous self, the stability of words, reason, and the possibility of determinable meanings. Without quite arguing that More was a postmodernist avant la lettre, this essay suggests that he was not a “humanist” who stalks the pages of much recent postmodernist theory and that in fact even while remaining a devout Catholic and sensible lawyer he was quite as aware as any recent critic of the slipperiness of human selves and human language. It is time that literary critics tightened up their definition of “humanist,” especially when writing about the Renaissance.

scholarly journals Influence of study model, baseline catalytic concentrations and analytical system on the stability of serum alanine aminotransferase

2020 ◽  
Vol 1 (2) ◽  
Author(s):  
Josep Miquel Bauça ◽  
Andrea Caballero ◽  
Carolina Gómez ◽  
Débora Martínez-Espartosa ◽  
Isabel García del Pino ◽  
...  
Keyword(s):  
Alanine Aminotransferase ◽  
Experimental Models ◽  
Individual Variability ◽  
Serum Samples ◽  
Multicentric Study ◽  
Different Temperatures ◽  
The Stability ◽  
Analytical System ◽  
Definition Of ◽  
Analytical Platforms

AbstractObjectivesThe stability of the analytes most commonly used in routine clinical practice has been the subject of intensive research, with varying and even conflicting results. Such is the case of alanine aminotransferase (ALT). The purpose of this study was to determine the stability of serum ALT according to different variables.MethodsA multicentric study was conducted in eight laboratories using serum samples with known initial catalytic concentrations of ALT within four different ranges, namely: <50 U/L (<0.83 μkat/L), 50–200 U/L (0.83–3.33 μkat/L), 200–400 U/L (3.33–6.67 μkat/L) and >400 U/L (>6.67 μkat/L). Samples were stored for seven days at two different temperatures using four experimental models and four laboratory analytical platforms. The respective stability equations were calculated by linear regression. A multivariate model was used to assess the influence of different variables.ResultsCatalytic concentrations of ALT decreased gradually over time. Temperature (−4%/day at room temperature vs. −1%/day under refrigeration) and the analytical platform had a significant impact, with Architect (Abbott) showing the greatest instability. Initial catalytic concentrations of ALT only had a slight impact on stability, whereas the experimental model had no impact at all.ConclusionsThe constant decrease in serum ALT is reduced when refrigerated. Scarcely studied variables were found to have a significant impact on ALT stability. This observation, added to a considerable inter-individual variability, makes larger studies necessary for the definition of stability equations.

scholarly journals Causality and stability conditions of a conformal charged fluid

2020 ◽  
Vol 2020 (8) ◽  
Author(s):  
Farid Taghinavaz
Keyword(s):  
Chemical Potential ◽  
Second Law Of Thermodynamics ◽  
Dense Medium ◽  
Wave Number ◽  
Second Law ◽  
Stability Conditions ◽  
Charged Fluid ◽  
Large Wave ◽  
The Stability ◽  
Large Wave Number

Abstract In this paper, I study the conditions imposed on a normal charged fluid so that the causality and stability criteria hold for this fluid. I adopt the newly developed General Frame (GF) notion in the relativistic hydrodynamics framework which states that hydrodynamic frames have to be fixed after applying the stability and causality conditions. To do this, I take a charged conformal matter in the flat and 3 + 1 dimension to analyze better these conditions. The causality condition is applied by looking to the asymptotic velocity of sound hydro modes at the large wave number limit and stability conditions are imposed by looking to the imaginary parts of hydro modes as well as the Routh-Hurwitz criteria. By fixing some of the transports, the suitable spaces for other ones are derived. I observe that in a dense medium having a finite U(1) charge with chemical potential μ0, negative values for transports appear and the second law of thermodynamics has not ruled out the existence of such values. Sign of scalar transports are not limited by any constraints and just a combination of vector transports is limited by the second law of thermodynamic. Also numerically it is proved that the most favorable region for transports $$ {\tilde{\upgamma}}_{1,2}, $$ γ ˜ 1 , 2 , coefficients of the dissipative terms of the current, is of negative values.

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