Related papers: Stability conditions on curves

We prove that, for a natural class of Bridgeland stability conditions on $\mathbb{P}^1\times\mathbb{P}^1$ and the blow-up of $\mathbb{P}^2$ at a point, the moduli spaces of Bridgeland semistable objects are projective. Our technique is to…

In this paper, we describe the spaces of stability conditions for the triangulated categories associated to three dimensional Calabi-Yau fibrations. We deal with two cases, the flat elliptic fibrations and smooth K3 (Abelian) fibrations. In…

This paper is an expository account of the theory of stable infinity categories. We prove that the homotopy category of a stable infinity category is triangulated, and that the collection of stable infinity categories is closed under a…

We consider an aggregation model for two interacting species. The coupling between the species is via their velocities, that incorporate self- and cross-interactions. Our main interest is categorizing the possible steady states of the…

We study three methods that prove the positivity of a natural numerical invariant associated to $1-$parameter families of polarized varieties. All these methods involve different stability conditions. In dimension 2 we prove that there is a…

The moduli space of slope-stable vector bundles on a normal projective variety over an algebraically closed field of characteristic $p\geq 0$ is stratified with respect to the decomposition type. On a smooth projective curve of genus at…

We give necessary conditions on the invariants (d,g) of a smooth, integral curve self-linked by a complete intersection of type (a,b) in projective three space. Similar conditions are given for s.t.c.i. curves with a multiplicity three…

We study the notion of stochastic stability with respect to diffusive perturbations for flows with smooth invariant measures. We investigate the question fully for non-singular flows on the circle. We also show that volume-preserving flows…

We describe the closure of the strata of abelian differentials with prescribed type of zeros and poles, in the projectivized Hodge bundle over the Deligne-Mumford moduli space of stable curves with marked points. We provide an explicit…

The problem of homological stability helps us to catch the structure of group homology. We calculate homological stability of special orthogonal groups, and we also calculate the stability of orthogonal groups with determinant-twisted…

We shall study the chamber structure of positive cone of the albanese fiber of the moduli spaces of stable objects on an abelian surfaces via the chamber structure of stability conditions.

We consider Bridgeland stability conditions for three-folds conjectured by Bayer-Macr\`i-Toda in the case of Picard rank one. We study the differential geometry of numerical walls, characterizing when they are bounded, discussing possible…

We give a brief overview of Bridgeland's theory of stability conditions, focusing on applications to algebraic geometry. We sketch the basic ideas in Bayer's proof of the Brill--Noether Theorem and in the authors' proof of a theorem by…

We introduce the abstract notion of a \emph{smoothable fine compactified Jacobian} of a nodal curve, and of a family of nodal curves whose general element is smooth. Then we introduce the notion of a combinatorial stability condition for…

Let $\mathrm{h}\mathscr{C}$ be the homotopy category of a stable infinity category $\mathscr{C}$. Then the homotopy category $\mathrm{h}\mathscr{C}^{\Delta^{1}}$ of morphisms in the stable infinity category $\mathscr{C}$ is also…

We study the strict stability of calibrated cones with an isolated singularity. For special Lagrangian cones and coassociative cones, we prove the strict stability. In the complex case, we give non-strictly stable examples.

Let $\mathcal{C}$ be a triangulated category with a proper class $\xi$ of triangles. Asadollahi and Salarian introduced and studied $\xi$-Gorenstein projective and $\xi$-Gorenstein injective objects, and developed Gorenstein homological…

We show that for any stable sheaf $E$ of slope $> 2g-1$ on a smooth, projective curve of genus $g$, the associated Picard sheaf $\hat{E}$ on the Picard variety of the curve is stable. We introduce a homological tool for testing…

We study fundamental group of the exchange graphs for the bounded derived category D(Q) of a Dynkin quiver Q and the finite-dimensional derived category D(\Gamma_N Q) of the Calabi-Yau-N Ginzburg algebra associated to Q. In the case of…

We consider the stack of stable curves of genus g with a given dual graph and we give an explicit desingularization of its closure in the moduli stack of stable curves. We study in particular the one-dimensional substack of curves with at…