Speaker
Description
Instanton bundles carry rich geometric data of a Fano threefold $X$. For instance, for low charge their moduli spaces are related to the fibres of the period map: this was shown by A. Iliev and D. Markushevich for threefolds of genus 8 -- we will review ongoing work with A. Verra for the case of genus 10.
Depending on the parity of the index of $X$, these bundles exhibit different behaviour, yet their moduli spaces share some common features which I will review, starting with the monadic description.
A conjecture of A. Kuznetsov implies that, for some specific charges, there should be a correspondence between even and odd instantons moduli inducing a birational transformation of the associated projective bundles over threefolds having equivalent Kuznetsov categories. I will discuss work in progress with S. Zhang and S. Feyzbakhsh about this conjecture for genus 10 and 12.
