A twistor correspondence for homogeneous polynomial differential operators
In three and four dimensions solutions of certain linear differential equations are known to correspond to cohomology classes on complex manifolds known as 'twistor spaces'. In this paper such a twistor correspondence is established between solutions of differential operators on \({\mathbb{C}}^{n+1}\) for \(n>1\) of the form \(D=f(\partial /\partial x_ 1,\partial /\partial x_ 2,...,\partial /\partial x_{n+1})\), where f is a homogeneous polynomial of degree k, and certain cohomology classes on a twistor space Z. The space Z is the total space of the hyperplane bundle restricted to the subvariety of \({\mathbb{P}}_ n\) determined by the zeroes of the polynomial f. When 1\(\leq k\leq n\) this correspondence is shown to be an isomorphism.
homogeneous polynomial differential operators
scientific article; zbMATH DE number 3873704