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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…
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…
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…
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…