Related papers: Serre dimension and stability conditions

We provide a categorical interpretation of a well-known identity from linear algebra as an isomorphism of certain functors between triangulated categories arising from finite dimensional algebras. As a consequence, we deduce that the Serre…

We construct a subset of the space of stability conditions for any projective threefold with an ample polarization that satisfies a certain Bogomolov-Gieseker inequality to refine the result in arXiv:1410.1585. Then, we demonstrate that the…

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…

In this paper, we study the space of stability conditions on a certain $N$-Calabi-Yau ($\text{CY}_N$) category associated to an $A_n$-quiver. Recently, Bridgeland and Smith constructed stability conditions on some $\text{CY}_3$ categories…

This chapter explores the notion of "dimension" of a set. Various power laws by which an Euclidean space can be characterized are used to define dimensions, which then explore different aspects of the set. Also discussed are the…

Inspired by mirror symmetry, we investigate some differential geometric aspects of the space of Bridgeland stability conditions on a Calabi-Yau triangulated category. The aim is to develop theory of Weil-Petersson geometry on the stringy…

This is a survey on two closely related subjects. First, we review the study of topological structure of `finite type' components of spaces of Bridgeland's stability conditions on triangulated categories. The key is to understand…

We construct Bridgeland stability conditions on the the following hyper-K\"ahler or strict Calabi--Yau manifolds: - Generalized Kummer varieties associated to an abelian surface that is isogenous to a product of elliptic curves. - Universal…

Let $X$ be a cubic threefold, quartic double solid or Gushel--Mukai threefold, and $\mathcal{K}u(X)\subset \mathrm{D}^b(X)$ be its Kuznetsov component. We show that a stability condition $\sigma$ on $\mathcal{K}u(X)$ is Serre-invariant if…

We describe spaces of Bridgeland stability conditions on certain triangulated categories associated to Coxeter systems. These categories are defined algebraically using the category of modules for zigzag algebras associated to Coxeter…

A noncommutative projective variety is defined, after Artin and Zhang, by a graded coherent algebra A, where the category of coherent sheaves is the quotient qgr(A) of the category of finitely presented graded modules by the subcategory of…

A numerical study of the $d$-dimensional Eddy Damped Quasi-Normal Markovian equations is performed to investigate the dependence on spatial dimension of homogeneous isotropic fluid turbulence. Relationships between structure functions and…

In this paper we study the dimension theory of planar self-affine sets satisfying dominated splitting in the linear parts and strong separation condition. The main results of this paper is the existence of dimension maximizing Gibbs…

We introduce a class of proper differential graded algebras which we call Serre cyclotomic. They generalize fractionally Calabi-Yau algebras and categorify de la Pe\~na's algebras of cyclotomic type. Path algebras of affine type and…

We apply a conjectured inequality on third chern classes of stable two-term complexes on threefolds to Fujita's conjecture. More precisely, the inequality is shown to imply a Reider-type theorem in dimension three which in turn implies that…

Using results in a previous paper "Non-semistable exceptional objects in hereditary categories", we focus here on studying the topology of the space of Bridgeland stability conditions on $D^b(Rep_k(Q ))$, where $Q$ is the acyclic triangular…

We give a sufficient condition for the Fourier dimension of a countable union of sets to equal the supremum of the Fourier dimensions of the sets in the union, and show by example that the Fourier dimension is not countably stable in…

We study the pointwise dimension for a new class of projection measures on arbitrary fractal limit sets without separation conditions. We prove that the pointwise dimension exists a.e. for this class of measures associated to equilibrium…

The Fourier dimension is not in general stable under finite unions of sets. Moreover, the stability of the Fourier dimension on particular pairs of sets is independent from the stability of the compact Fourier dimension.

This paper sheds new light on several interrelated topics of second-order variational analysis, both in finite and infinite-dimensional settings. We establish new relationships between second-order growth conditions on functions, the basic…