65 citations · 351 across the 37 of their papers we have counts for
41 papers · 1 filter
Stability conditions and moduli spaces on projective families
Chunyi Li, Zhiyu Liu, Ziqi Liu +4
We extend the construction of stability conditions on projective schemes over a field to projective families over an arbitrary base, and prove that they admit proper relative modul…
Metrics on triangulated categories and their enhancements
Alberto Canonaco, Amnon Neeman, Paolo Stellari
In this paper we investigate the uniqueness of enhancements of the natural subcategories of weakly approximable triangulated categories. The main idea is to enhance at the level of…
Hyper-Kähler varieties: Lagrangian fibrations, atomic sheaves, and categories
Alessio Bottini, Emanuele Macrì, Paolo Stellari
We review recent developments in the theory of compact hyper-Kähler varieties, from the viewpoint of Lagrangian fibrations, moduli spaces of stable sheaves, and derived categories.…
Stability conditions on products of curves and Hilbert schemes of surfaces
Chunyi Li, Emanuele Macrì, Alexander Perry +2
We prove that stability conditions on the derived category of a product of curves of positive genus are uniquely determined by their central charge and the phase of skyscraper shea…
Strong uniqueness of enhancements for the dual numbers: a case study
Alberto Canonaco, Amnon Neeman, Paolo Stellari
We prove that the bounded and bounded below derived categories of (all) modules over the dual numbers have strongly unique (dg) enhancements. To this end we relate those categories…
Weakly approximable triangulated categories and enhancements: a survey
Alberto Canonaco, Amnon Neeman, Paolo Stellari
This paper surveys some recent results, concerning the intrinsicness of natural subcategories of weakly approximable triangulated categories. We also review the results about uniqu…
The passage among the subcategories of weakly approximable triangulated categories
Alberto Canonaco, Christian Haesemeyer, Amnon Neeman +1
In this article we prove that all the inclusions between the 'classical' and naturally defined full triangulated subcategories of a weakly approximable triangulated category are in…
Categorical Torelli theorems: results and open problems
Laura Pertusi, Paolo Stellari
We survey some recent results concerning the so called Categorical Torelli problem. This is to say how one can reconstruct a smooth projective variety up to isomorphism, by using t…
A Refined Derived Torelli Theorem for Enriques surfaces, II: the non-generic case
Chunyi Li, Paolo Stellari, Xiaolei Zhao
We prove that two Enriques surfaces defined over an algebraically closed field of characteristic different from are isomorphic if their Kuznetsov components are equivalent. Thi…
Uniqueness of enhancements for derived and geometric categories
Alberto Canonaco, Amnon Neeman, Paolo Stellari
We prove that the derived categories of abelian categories have unique enhancements -- all of them, the unbounded, bounded, bounded above and bounded below derived categories. The…
A refined Derived Torelli Theorem for Enriques surfaces
Chunyi Li, Howard Nuer, Paolo Stellari +1
We prove that two general Enriques surfaces defined over an algebraically closed field of characteristic different from are isomorphic if their Kuznetsov components are equival…
Stability conditions in families
Arend Bayer, Martí Lahoz, Emanuele Macrì +3
We develop a theory of Bridgeland stability conditions and moduli spaces of semistable objects for a family of varieties. Our approach is based on and generalizes previous work by…
Localizations of the category of categories and internal Homs
Alberto Canonaco, Mattia Ornaghi, Paolo Stellari
We prove that the localizations of the categories of dg categories, of cohomologically unital and strictly unital categories with respect to the corresponding classes of…
Lectures on non-commutative K3 surfaces, Bridgeland stability, and moduli spaces
Emanuele Macrì, Paolo Stellari
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 s…
Stability conditions on Kuznetsov components
Arend Bayer, Martí Lahoz, Emanuele Macrì +1
We introduce a general method to induce Bridgeland stability conditions on semiorthogonal components of triangulated categories. In particular, we prove the existence of Bridgeland…
Generalized twisted cubics on a cubic fourfold as a moduli space of stable objects
Martí Lahoz, Manfred Lehn, Emanuele Macrì +1
We revisit the work of Lehn-Lehn-Sorger-van Straten on twisted cubic curves in a cubic fourfold not containing a plane in terms of moduli spaces. We show that the blow-up alon…
A tour about existence and uniqueness of dg enhancements and lifts
Alberto Canonaco, Paolo Stellari
This paper surveys the recent advances concerning the relations between triangulated (or derived) categories and their dg enhancements. We explain when some interesting triangulate…
Uniqueness of dg enhancements for the derived category of a Grothendieck category
Alberto Canonaco, Paolo Stellari
We prove that the derived category of a Grothendieck abelian category has a unique dg enhancement. Under some additional assumptions, we show that the same result holds true for it…
ACM bundles on cubic threefolds
Martí Lahoz, Emanuele Macrì, Paolo Stellari
We study ACM bundles on cubic threefolds by using derived category techniques. We prove that the moduli space of stable Ulrich bundles of any rank is always non-empty by showing th…
The Space of Stability Conditions on Abelian Threefolds, and on some Calabi-Yau Threefolds
Arend Bayer, Emanuele Macrì, Paolo Stellari
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…
Internal Homs via extensions of dg functors
Alberto Canonaco, Paolo Stellari
We provide a simple proof of the existence of internal Homs in the localization of the category of dg categories with respect to all quasi-equivalences and of some of their main pr…
ACM bundles on cubic fourfolds containing a plane
Martí Lahoz, Emanuele Macrì, Paolo Stellari
We study ACM bundles on cubic fourfolds containing a plane exploiting the geometry of the associated quadric fibration and Kuznetsov's treatment of their bounded derived categories…
Fourier-Mukai functors: a survey
Alberto Canonaco, Paolo Stellari
This paper surveys some recent results about Fourier--Mukai functors. In particular, given an exact functor between the bounded derived categories of coherent sheaves on two smooth…
Does full imply faithful?
Alberto Canonaco, Dmitri Orlov, Paolo Stellari
We study full exact functors between triangulated categories. With some hypotheses on the source category we prove that it admits an orthogonal decomposition into two pieces such t…