Related papers: Stability conditions and extremal contractions

We give a complete classification of semistable rank two sheaves on three-dimensional projective space with maximal third Chern character. This implies an explicit description of their moduli spaces. As an open subset they contain rank two…

We find locally free resolutions of length one for all semi-stable sheaves supported on curves of multiplicity five in the complex projective plane. In some cases we also find geometric descriptions of these sheaves by means of extensions.…

We prove that moduli spaces of torsion-free sheaves on a projective smooth complex surface are irreducible, reduced and of the expected dimension, provided the expected dimension is large enough. Actually we prove more: given a line bundle…

On a normal projective variety the locus of $\mu$-stable bundles that remain $\mu$-stable on all Galois covers prime to the characteristic is open in the moduli space of Gieseker semi-stable sheaves. On a smooth projective curve of genus at…

We give sufficient conditions for the (semi-)stability of torsion free sheaves on a primitive multiple curve. These conditions are used to prove that some moduli spaces of stable sheaves are not empty. We study mainly the quasi locally free…

This is the first of two papers studying moduli spaces of a certain class of coherent sheaves, which we call {\it stable perverse coherent sheaves}, on the blowup of a projective surface. They are used to relate usual moduli spaces of…

For any smooth projective variety $X$ of dimension $n$ over an algebraically closed field $k$ of characteristic $p>0$ with $\mu(\Omega^1_X)>0$. If ${\rm T}^{\ell}(\Omega^1_X)$ ($0<\ell<n(p-1)$) are semi-stable, then the sheaf $B^1_X$ of…

We prove the existence of fine moduli spaces of simple coherent sheaves on families of irreducible curves. Our proof is based on the existence of a universal upper bound of the Castelnuovo-Mumford regularity of such sheaves, which we…

We classify Chern characters of semistable sheaves up to rank four in three dimensional projective space. As a corollary we show that moduli spaces of semistable sheaves between rank zero and four with maximal third Chern character are…

Let $X$ be a smooth projective variety over $\mathbb C$. In this paper, we prove that $\mathrm{D}^b(X)$, the bounded derived category of coherent sheaves on $X$, always admits stability conditions in the sense of Bridgeland.

We study the moduli space of stable sheaves of Euler characteristic 1, supported on curves of arithmetic genus 2 contained in a smooth quadric surface. We show that this moduli space is rational. We give a classification of the stable…

We investigate a semi-continuity property for stability conditions for sheaves that is important for the problem of variation of the moduli spaces as the stability condition changes. We place this in the context of a notion of stability…

In this paper, we first show that for an acyclic gentle algebra A, the irreducible components of any moduli space of A-modules are products of projective spaces. Next, we show that the nice geometry of the moduli spaces of modules of an…

We show that the moduli space of semi-stable sheaves on a smooth quadric surface, having dimension 1, multiplicity 4, Euler characteristic 2, and first Chern class (2, 2), is the blow-up at two points of a certain hypersurface in a weighted…

We construct explicit examples of elementary extremal contractions, both birational and of fiber type, from smooth projective n-dimensional varieties, n\geq 4, onto smooth projective varieties, arising from classical projective geometry and…

We introduce a notion of Gieseker stability for coherent sheaves on tame Deligne-Mumford stacks with projective moduli scheme and some chosen generating sheaf on the stack in the sense of Olsson and Starr \cite{MR2007396}. We prove that…

This note revisits stability conditions on the bounded derived categories of coherent sheaves on irreducible projective curves. In particular, all stability conditions on smooth curves are classified and a connected component of the…

We describe stability conditions for pairs consisting of a coherent sheaf and a homomorphism to a fixed coherent sheaf on a projective variety. The corresponding moduli spaces are constructed for pairs on curves and surfaces. We consider…

We study the moduli space of stable sheaves of Euler characteristic 1 supported on curves of arithmetic genus 3 contained in a smooth quadric surface. We show that this moduli space is rational. We compute its Betti numbers by studying the…

This article deals with the quotient category of the category of coherent sheaves on an irreducible smooth projective variety by the full subcategory of sheaves supported in codimension greater than c. It turns out that this category has…