相关论文: Stability conditions on surface root stacks

This paper is largely concerned with constructing coarse moduli spaces for Artin stacks. The main purpose of this paper is to introduce the notion of stability on an arbitrary Artin stack and construct a coarse moduli space for the open…

We prove that some of the classical homological stability results for configuration spaces of points in manifolds can be lifted to motivic cohomology.

We study the space of smooth marked hypersurfaces in a given linear system. Specifically, we prove a homology h-principle to compare it with a space of sections of an appropriate jet bundle. Using rational models, we compute its rational…

We study stable rationality properties of conic bundles over rational surfaces.

Let X be a compact connected Riemann surface of genus at least two. We compute the Chen--Ruan cohomology ring of the moduli space of stable PSL(2, C)--bundles of nontrivial second Stiefel--Whitney class over X.

Using Bridgeland stability conditions we give sufficient criteria for a stable vector bundle on a surface to remain stable when restricted to a curve. We give a stronger criterion when the vector bundle is a general vector bundle on the…

In this work we describe the Chen-Ruan cohomology of the moduli stacks of smooth and stable genus 2 pointed curves, and its algebraic counterpart: the stringy Chow ring. In the first half of the paper we compute the additive structure of…

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.

We study rationality properties of quadric surface bundles over the projective plane. We exhibit families of smooth projective complex fourfolds of this type over connected bases, containing both rational and non-rational fibers.

We study Brauer-Severi surface bundles over smooth projective varieties via root stacks, with a view towards applications to failure of stable rationality.

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.

We show a stability-type theorem for foliations on projective spaces which arise as pullbacks of foliations with a split tangent sheaf on weighted projective spaces. As a consequence, we will be able to construct many irreducible components…

We exhibit families of smooth projective threefolds with both stably rational and non stably rational fibers.

We prove an existence result for stable vector bundles with arbitrary rank on an algebraic surface, and determine the birational structure of certain moduli space of stable bundles on a rational ruled surface.

We prove a motivic stabilization result for the cohomology of the local systems on configuration spaces of varieties over $\mathbb{C}$ attached to character polynomials. Our approach interprets the stabilization as a probabilistic…

We prove stability of rank two tautological bundles on the Hilbert square of a surface (under a mild positivity condition) and compute their Chern classes.

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…

We show cocycle stability for linear maps with a weak irreducibility condition and their jointly integrable perturbations.

Let $(X,\,D)$ be an $m$-pointed compact Riemann surface of genus at least $2$. For each $x \,\in\, D$, fix full flag and concentrated weight system $\alpha$. Let $P \mathcal{M}_{\xi}$ denote the moduli space of semi-stable parabolic vector…

With the rise of network science old topics in ecology and economics are resurfacing. One such topic is structural stability (often referred to as qualitative stability or sign stability). A system is deemed structurally stable if the…