The moduli of super-null correlation bundles on \({\mathbb P}_ 3\)
Let \(M_ 2(c_ 1,c_ 2)\) denote the coarse moduli scheme of stable rank two vector bundles on \({\mathbb{P}}_ 3({\mathbb{C}})\) with fixed Chern classes. The paper is concerned with one particular component of \(M_ 2(0,c_ 2)\). Using only the properties of the spectrum of such bundles on \({\mathbb{P}}_ 3\) an irreducible, rational and generically nonsingular component is shown to exist in \(M_ 2(0,(k+1)^ 2)\). The general bundle of this component is the pull-back of a null-correlation bundle on \({\mathbb{P}}_ 3\) via the morphism of \({\mathbb{P}}_ 3\) onto \({\mathbb{P}}_ 3\) defined by the linear system of hyperplanes of degree \(k+1\) on the underlying \({\mathbb{P}}_ 3\). The method uses the general technique of reduction on unstable surfaces. The dimension of super-null-correlations component is \(8c_ 2-3+4h^ 0{\mathcal X}(-3)\), where \({\mathcal X}\) is the spectrum of type \({\mathcal X}^+=0^{k+1}1^ k...(k-1)^ 2k^ 1\) (positive part).
coarse moduli scheme of stable rank two vector bundles
dimension of super-null-correlations component
scientific article; zbMATH DE number 3959612
scientific article