Related papers: Bridgeland stability conditions and skew lines on …
Following up on the construction of Bridgeland stability condition on $\mathbb{P}^3$ by Macr\`i, we develop techniques to study concrete wall crossing behavior for the first time on a threefold. In some cases, such as complete intersections…
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 study the birational geometry of the Hilbert scheme of n points on P^2. We discuss the stable base locus decomposition of the effective cone and the corresponding birational models. We give modular interpretations to the…
We give another proof of Le Potier's result and some variants on moduli spaces of semistable sheaves on the projective plane, using the Bridgeland stability conditions. As an application we study the wall-crossing phenomena of the Hilbert…
We study wall crossings in Bridgeland stability for the Hilbert scheme of elliptic quartic curves in three dimensional projective space. We provide a geometric description of each of the moduli spaces we encounter, including when the second…
We study the Hilbert scheme of twisted cubics in the three-dimensional projective space by using Bridgeland stability conditions. We use wall-crossing techniques to describe its geometric structure and singularities, which reproves the…
Over the last few years, wall-crossing for Bridgeland stability conditions has led to a large number of results in algebraic geometry, particular on birational geometry of moduli spaces. We illustrate some of the methods behind these result…
We give a natural family of Bridgeland stability conditions on the derived category of a smooth projective complex surface S and describe ``wall-crossing behavior'' for objects with the same invariants as $\cO_C(H)$ when H generates Pic(S)…
We construct a family of nef divisor classes on every moduli space of stable complexes in the sense of Bridgeland. This divisor class varies naturally with the Bridgeland stability condition. For a generic stability condition on a K3…
This paper studies wall crossings in Bridgeland stability for the moduli space of Pandharipande--Thomas stable pairs associated with quintic genus 2 curves in the complex projective three-space. We provide a complete list of irreducible…
We investigate the wall-crossing behavior as Bridgeland moduli spaces for some Simpson moduli spaces of Gieseker-semistable torsion sheaves on $\mathbb{P}^1\times \mathbb{P}^1$ with linear Hilbert polynomial. In particular, we recover some…
We study projectivity of moduli spaces on the DT/PT wall crossing in Bridgeland and polynomial stability on a smooth, projective threefold. First, we construct a globally generated line bundle on the moduli stack of higher-rank…
Let $X$ be a smooth complex projective variety. In 2002, Bridgeland defined a notion of stability for the objects in $D^b(X)$, the bounded derived category of coherent sheaves on $X$, which generalized the notion of slope stability for…
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…
We show that the wall-crossing in Bridgeland stability fails to be detected by the birational geometry of stable sheaves, and vice versa. There is a wall in the stability space of canonical genus four curves which does not induce a step in…
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 compute moduli spaces of Bridgeland stable objects on an irreducible principally polarized complex abelian surface corresponding to twisted ideal sheaves. We use Fourier-Mukai techniques to extend the ideas of Arcara and Bertram to…
Moduli spaces of sheaves and Hilbert schemes of points have experienced a recent resurgence in interest in the past several years, due largely to new techniques arising from Bridgeland stability conditions and derived category methods. In…
Let $(X,H)$ be a smooth, projective, polarized surface over $\mathbb{C}$, and let $v \in K_{\mathrm{num}}(X)$ be a class of positive rank. We prove that for certain Bridgeland stability conditions $\sigma = (\mathcal{A}, Z)$ "on the…
We apply Bridgeland stability conditions machinery to describe the geometry of some classical moduli spaces associated with canonical genus four curves in $\mathbb{P}^3$ via an effective control over its wall-crossing. These moduli spaces…