Related papers: Stability conditions on Kuznetsov components

Let $M$ denote a specific cubic fourfold that accommodates a group action by $\mathbb{Z}/3\mathbb{Z}$. Through utilization of derived Mckay correspondence, we present a new proof establishing the identification of the equivariant Kuznetsov…

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…

By the description due to Mukai and Iliev, a smooth prime Fano threefold X of genus 9 is associated to a surface P(V), ruled over a smooth plane quartic Gamma. We use Kuznetsov's integral functor to study rank-2 stable sheaves on X with odd…

The Kuznetsov component of the derived category of a cubic fourfold is a `non-commutative K3 surface'. Its symmetric square is hence a `non-commutative hyperkaehler fourfold'. We prove that this category is equivalent to the derived…

We prove a Bogomolov-Gieseker type inequality for the third Chern characters of stable sheaves on Calabi-Yau 3-folds and a large class of Fano 3-folds with given rank and first and second Chern classes. The proof uses the spreading-out…

We provide Lyapunov-like characterizations of boundedness and convergence of non-trivial solutions for a class of systems with unstable invariant sets. Examples of systems to which the results may apply include interconnections of stable…

A thin and narrow rectangular plate having the two short edges hinged and the two long edges free is considered. A nonlinear nonlocal evolution equation describing the deformation of the plate is introduced: well-posedness and existence of…

We investigate the behaviour of Bridgeland stability conditions under change of base field with particular focus on the case of finite Galois extensions. In particular, we prove that for a variety X over a field K and a finite Galois…

We prove nonlinear asymptotic stability of steady spheres in the two-phase Stefan problem with surface tension. Our method relies on the introduction of appropriate orthogonality conditions in conjunction with a high-order energy method.

We give a simple criterion for slope stability of Fano manifolds $X$ along divisors or smooth subvarieties. As an application, we show that $X$ is slope stable along an ample effective divisor $D\subset X$ unless $X$ is isomorphic to a…

We study the space of stability conditions attached to the derived category of $A_{n}$-mod for $A_{n}$ the Brauer tree algebra of the line with $n$ edges. These algebras arise in the study of cyclic defect blocks of group algebras, and they…

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…

The equation arising from Prandtl boundary layer theory is considered. The existence of the entropy solution can be proved by BV estimate method. The interesting problem is that, since a may be degenerate on the boundary, the usual boundary…

We prove that the alpha invariant of a quasi-smooth Fano 3-fold weighted hypersurface of index $1$ is greater than or equal to $1/2$. Combining this with the result of Stibitz and Zhuang \cite{SZ19} on a relation between birational…

The present paper proposes a new condition to replace both the ($O$-regularly varying) quasimonotone condition and a certain type of bounded variation condition, and shows the same conclusion for the uniform convergence of certain…

We shall study some moduli spaces of Bridgeland's semi-stable objects on abelian surfaces and K3 surfaces with Picard number 1. Under some conditions, we show that the moduli spaces are isomorphic to the moduli spaces of Gieseker…

We give a new proof of the following theorem: moduli spaces of stable complexes on a complex projective K3 surface, with primitive Mukai vector and with respect to a generic Bridgeland stability condition, are hyperk\"{a}hler varieties of…

In this paper we introduce the notion of a 'generalised' co-slicing of a triangulated category. This generalises the theory of co-stability conditions in a manner analogous to the way in which Gorodentsev, Kuleshov and Rudakov's…

We prove exponential stability theorems of Nekhoroshev type for motion in the neighbourhood of an elliptic fixed point in Hamiltonian systems having an additional transverse component of arbitrary dimension.

We study moduli spaces of stable objects in the Kuznetsov components of Fano threefolds. We prove a general non-emptiness criterion for moduli spaces, which applies to the cases of prime Fano threefolds of index $1$, degree $10 \leq d \leq…