21 citations · 52 across the 14 of their papers we have counts for
19 papers
-cycles and sheaves on abelian surfaces
Giovanni Mongardi, Gianluca Pacienza, Laura Pertusi
We introduce a filtration on the Chow ring of an abelian surface , inspired by O'Grady's filtration on K3 surfaces. We give a geometric description of the filtration, and we pro…
Noncommutative varieties and stability conditions: an overview
Laura Pertusi
Using the modern perspective of noncommutative algebraic geometry we survey some recent progress in the theory of stability conditions and moduli spaces with applications in hyperk…
Higher dimensional moduli spaces on Kuznetsov components of Fano threefolds
Chunyi Li, Yinbang Lin, Laura Pertusi +1
We study moduli spaces of stable objects in the Kuznetsov components of Fano threefolds. We prove a general non-emptiness criterion for moduli spaces, which applies to the cases of…
Irreducible symplectic varieties via relative Prym varieties
Emma Brakkee, Chiara Camere, Annalisa Grossi +3
Generalizing work of Markushevich--Tikhomirov and Arbarello--Saccà--Ferretti, we use relative Prym varieties to construct Lagrangian fibered symplectic varieties in infinitely many…
Some remarks about deformation theory and formality conjecture
Huachen Chen, Laura Pertusi, Xiaolei Zhao
Using the algebraic criterion proved by Bandiera, Manetti and Meazzini, we show the formality conjecture for universally gluable objects with linearly reductive automorphism groups…
Moduli spaces of stable objects in Enriques categories
Alexander Perry, Laura Pertusi, Xiaolei Zhao
We study moduli spaces of stable objects in Enriques categories by exploiting their relation to moduli spaces of stable objects in associated K3 categories. In particular, we settl…
Kernels of categorical resolutions of nodal singularities
Warren Cattani, Franco Giovenzana, Shengxuan Liu +4
In this paper we study derived categories of nodal singularities. We show that for all nodal singularities there is a categorical resolution whose kernel is generated by a or $…
Derived categories of hearts on Kuznetsov components
Chunyi Li, Laura Pertusi, Xiaolei Zhao
We prove a general criterion which guarantees that an admissible subcategory of the derived category of an abelian category is equivalent to the bounded derived categ…
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…
Stability conditions on Kuznetsov components of Gushel-Mukai threefolds and Serre functor
Laura Pertusi, Ethan Robinett
We show that the stability conditions on the Kuznetsov component of a Gushel-Mukai threefold, constructed by Bayer, Lahoz, Macrì and Stellari, are preserved by the Serre functor, u…
Serre-invariant stability conditions and Ulrich bundles on cubic threefolds
Soheyla Feyzbakhsh, Laura Pertusi
We prove a general criterion which ensures that a fractional Calabi--Yau category of dimension admits a unique Serre-invariant stability condition, up to the action of the…
Elliptic quintics on cubic fourfolds, O'Grady 10, and Lagrangian fibrations
Chunyi Li, Laura Pertusi, Xiaolei Zhao
For a smooth cubic fourfold Y, we study the moduli space M of semistable objects of Mukai vector in the Kuznetsov component of Y. We show that with a certain choice of…
Some remarks on Fano threefolds of index two and stability conditions
Laura Pertusi, Song Yang
We prove that ideal sheaves of lines in a Fano threefold of Picard rank one and index two are stable objects in the Kuznetsov component , with respect to the st…
Marked and labelled Gushel-Mukai fourfolds
Emma Brakkee, Laura Pertusi
We prove that the moduli stacks of marked and labelled Hodge-special Gushel-Mukai fourfolds are isomorphic. As an application, we construct rational maps from the stack of Hodge-sp…
Stability conditions and moduli spaces for Kuznetsov components of Gushel-Mukai varieties
Alexander Perry, Laura Pertusi, Xiaolei Zhao
We prove the existence of Bridgeland stability conditions on the Kuznetsov components of Gushel-Mukai varieties, and describe the structure of moduli spaces of Bridgeland semistabl…
Twisted cubics on cubic fourfolds and stability conditions
Chunyi Li, Laura Pertusi, Xiaolei Zhao
We give an interpretation of the Fano variety of lines on a cubic fourfold and of the hyperkahler eightfold, constructed by Lehn, Lehn, Sorger and van Straten from twisted cubic cu…
On the double EPW sextic associated to a Gushel-Mukai fourfold
Laura Pertusi
In analogy to the case of cubic fourfolds, we discuss the conditions under which the double cover of the EPW sextic hypersurface associated to a Gushel-Mukai fourfold…
Voevodsky's conjecture for cubic fourfolds and Gushel-Mukai fourfolds via noncommutative K3 surfaces
Mattia Ornaghi, Laura Pertusi
In the first part of this paper we will prove the Voevodsky's nilpotence conjecture for smooth cubic fourfolds and ordinary generic Gushel-Mukai fourfolds. Then, making use of nonc…
Fourier-Mukai partners for very general special cubic fourfolds
Laura Pertusi
We exhibit explicit examples of very general special cubic fourfolds with discriminant admitting an associated (twisted) K3 surface, which have non-isomorphic Fourier-Mukai par…