3 papers
math.AG2025
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…
math.AG2021
The Looijenga-Lunts-Verbitsky algebra and Verbitsky's Theorem
Alessio Bottini
In these notes we review some basic facts about the LLV Lie algebra. It is a rational Lie algebra, introduced by Looijenga-Lunts and Verbitsky, acting on the rational cohomology of…
math.AG2021
Stable Sheaves on K3 Surfaces via Wall-Crossing
Alessio Bottini
We give a new proof of the following theorem: moduli spaces of stable complexes on a complex projective K3 surface, with primitive Mukai vector and with respect to a generic Bridge…