3-instantons and lattices of quadrics (Q1318133)

For the projective 3-space \(\mathbb{P}\) over the complex numbers one considers the moduli space \(\mathbb{M}_ n\) of stable rank 2 bundles with Chern numbers \(c_ 1 = 0\) and \(c_ 2 = n\). The bundles which are \(n\)-instantons define an open subset \(\mathbb{I}_ n\) of \(\mathbb{M}_ n\). For \(n = 1\) and \(n = 2\) there exist geometric descriptions of these moduli spaces. The authors give a description of the moduli space of 3-instantons in terms of nets of quadrics in \(\mathbb{P}\). These nets can be identified with the Grassmannian \(G(2,9)\). The authors give an isomorphism of the open subset of 3-instantons without 3-jumping lines to the open subset of this Grassmannian corresponding to nets without a quadric which is degenerate in 2 planes and which is not a net of Lüroth type.