• Corpus ID: 232404566

Fullness of exceptional collections via stability conditions -- A case study: the quadric threefold

  title={Fullness of exceptional collections via stability conditions -- A case study: the quadric threefold},
  author={Barbara Bolognese and Domenico Fiorenza},
A powerful tool of investigation of Fano varieties is provided by exceptional collections in their derived categories. Proving the fullness of such a collection is generally a nontrvial problem, usually solved on a case-by-case basis, with the aid of a deep understanding of the underlying geometry. Likewise, when an exceptional collection is not full, it is not straightforward to determine whether its “residual” category, i.e., its right orthogonal, is the derived category of a variety. We show… 

A note on Bridgeland moduli spaces and moduli spaces of sheaves on $$X_{14}$$ and $$Y_3$$

<jats:p>We study Bridgeland moduli spaces of semistable objects of <jats:inline-formula><jats:alternatives><jats:tex-math>$$(-1)$$</jats:tex-math><mml:math



The space of stability conditions on abelian threefolds, and on some Calabi-Yau threefolds

We describe a connected component of the space of stability conditions on abelian threefolds, and on Calabi-Yau threefolds obtained as (the crepant resolution of) a finite quotient of an abelian

Projectivity and birational geometry of Bridgeland moduli spaces

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

On residual categories for Grassmannians

We define and discuss some general properties of residual categories of Lefschetz decompositions in triangulated categories. In the case of the derived category of coherent sheaves on the

Stability conditions on triangulated categories

This paper introduces the notion of a stability condition on a triangulated category. The motivation comes from the study of Dirichlet branes in string theory, and especially from M.R. Douglas's

Hodge theory and derived categories of cubic fourfolds

Cubic fourfolds behave in many ways like K3 surfaces. Certain cubics - conjecturally, the ones that are rational - have specific K3s associated to them geometrically. Hassett has studied cubics with


It is proved that a triangulated category generated by a strong exceptional collection is equivalent to the derived category of modules over an algebra of homomorphisms of this collection. For the

Lectures on Non-commutative K3 Surfaces, Bridgeland Stability, and Moduli Spaces

We survey the basic theory of non-commutative K3 surfaces, with a particular emphasis to the ones arising from cubic fourfolds. We focus on the problem of constructing Bridgeland stability conditions

The K3 category of a cubic fourfold

Smooth cubic hypersurfaces $X\subset \mathbb{P}^{5}$ (over $\mathbb{C}$ ) are linked to K3 surfaces via their Hodge structures, due to the work of Hassett, and via a subcategory

Spinor bundles on quadrics

We define some stable vector bundles on the complex quadric hypersurface Qn of dimension n as the natural generalization of the universal bundle and the dual of the quotient bundle on Q4 ~ Gr(l,3).

Stability conditions on Fano threefolds of Picard number 1

  • Chunyi Li
  • Mathematics
    Journal of the European Mathematical Society
  • 2018
We prove the conjectural Bogomolov-Gieseker type inequality for tilt slope stable objects on each Fano threefold X of Picard number one. Based on the previous works on Bridgeland stability