8 papers · 1 filter
The tangent bundle of a generalized Kummer fourfold is obstructed
Alessio Bottini
For a hyper-Kähler fourfold of generalized Kummer type, we construct an infinitesimal deformation of the tangent bundle with non-zero Yoneda square. This is the first exa…
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.…
Semi-rigid stable sheaves: a criterion and examples
Alessio Bottini, Riccardo Carini
Inspired by Mukai's work on K3 surfaces, we introduce and study a notion of semi-rigidity for stable sheaves on smooth polarised varieties, designed to capture the existence of sta…
The period-index problem for hyperkähler varieties: Lower and upper bounds
Alessio Bottini, Daniel Huybrechts
It is expected that a stronger form of the period-index conjecture holds for hyperkähler varieties. Following ideas of Hotchkiss, we provide further evidence for this expectation b…
Derived categories of Fano varieties of lines
Alessio Bottini, Daniel Huybrechts
We gather evidence for a conjecture of Galkin predicting the derived category of the Fano variety of lines contained in a smooth cubic fourfold to be equivalent to the Hilbert squa…
O'Grady's tenfolds from stable bundles on hyper-Kähler fourfolds
Alessio Bottini
We provide a modular construction of the Laza--Saccà--Voisin compactification of the intermediate Jacobian fibration of a cubic fourfold. Additionally, we construct infinitely many…