Related papers: Stability conditions for generic K3 categories
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…
This article studies Kummer K3 surfaces close to the orbifold limit. We improve upon estimates for the Calabi-Yau metrics due to R. Kobayashi. As an application, we study stable closed geodesics. We use the metric estimates to show how…
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 study type III contractions of Calabi-Yau threefolds containing a ruled surface over a smooth curve. We discuss the conditions necessary for the image threefold to by smoothable. We describe the change in Hodge numbers caused by this…
We prove some general statements on stability conditions of Calabi-Yau surfaces and discuss the stability manifold of the cotangent bundle of P^1. Our primary interest is in spherical objects.
Given a holomorphic family of Bridgeland stability conditions over a surface, we define a notion of spectral network which is an object in a Fukaya category of the surface with coefficients in a triangulated DG-category. These spectral…
Motivated by gauge theory on manifolds with exceptional holonomy, we construct examples of stable bundles on K3 surfaces that are invariant under two involutions: one is holomorphic; and the other is anti-holomorphic. These bundles are…
We introduce the notion of relative stability conditions on triangulated categories with respect to left admissible subcategories, based on arXiv:math/0212237, and demonstrate the deformation of relative stability conditions via the…
We prove the existence of Bridgeland stability conditions on the Kuznetsov components of Gushel-Mukai varieties, and describe the structure of moduli spaces of Bridgeland semistable objects in these categories in the even-dimensional case.…
We survey some aspects of stability conditions both in general and on the derived category of coherent sheaves on a surface, with applications to the birational geometry of certain holomorphic symplectic varieties.
The duality between $E_8\times E_8$ heteritic string on manifold $K3\times T^2$ and Type IIA string compactified on a Calabi-Yau manifold induces a correspondence between vector bundles on $K3\times T^2$ and Calabi-Yau manifolds. Vector…
We construct Bridgeland stability conditions on the derived category of smooth quasi-projective Deligne-Mumford surfaces whose coarse moduli spaces have ADE singularities. This unifies the construction for smooth surfaces and Bridgeland's…
Categorical resolutions of singularities are a replacement of resolution of singularities within the realm of triangulated categories. They allow the study of the derived category of a singular variety $X$ via a triangulated category that…
We construct new t-structures on the derived category of coherent sheaves on smooth projective threefolds. We conjecture that they give Bridgeland stability conditions near the large volume limit. We show that this conjecture is equivalent…
We consider stable minimal surfaces of genus 1 in Euclidean space and in Riemannian manifolds. Under the condition of covering stability (all finite covers are stable) we show that a genus 1 finite total curvature minimal surface in…
We show that certain classes of K3 fibered Calabi-Yau manifolds derive from orbifolds of global products of K3 surfaces and particular types of curves. This observation explains why the gauge groups of the heterotic duals are determined by…
The article revisits birational and biregular automorphisms of the Hilbert scheme of points on a K3 surface from the perspective of derived categories. Under the assumption that the K3 surface is generic, the birational and biregular…
In this paper, we prove a stronger form of the Bogomolov-Gieseker (BG) inequality for stable sheaves on two classes of Calabi-Yau threefolds, namely, weighted hypersurfaces inside the weighted projective spaces $\mathbb{P}(1, 1, 1, 1, 2)$…
Using wall-crossing for K3 surfaces, we establish birational equivalence of moduli spaces of stable objects on generic Enriques surfaces for different stability conditions. As an application, we prove in the case of a Mukai vector of odd…
Fix a polarised Calabi-Yau threefold $(X,H)$. We reduce a version of the Bayer-Macr\`i-Toda conjecture for $(X,H)$, which ensures the existence of Bridgeland stability conditions on $X$, to verifying a Brill-Noether-type inequality for…