7 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…
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 man…
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…