Speaker
Description
Let $X$ be a Fano threefold of Picard number one and of index $i_X$ . A rank 2 instanton sheaf of charge $k$ on $X$ is defined as a μ-semistable rank 2 torsion-free sheaf $F$ having Chern classes $c_1(F) = −r_X$, $c_2(F) = k$, $c_3(F) = 0$, with $r_X \in \{0,1\}$ such that $r_X \equiv i_X \bmod{2}$. Locally free instantons, originally defined on the projective space and later generalised on other Fano threefolds X, had been largely studied by several authors in the past years; their moduli spaces present an extremely rich geometry and useful applications to the study of curves on X. In this talk, I will illustrate several features of non-locally free instantons of low charge on 3-dimensional quadrics and cubics. I will focus in particular on the role that they play in the study of the Gieseker-Maruyama moduli space $M_X (2; −h, k, 0)$ and describe how we can still relate these sheaves to curves on $X$.
