The Penrose transform and the topology of certain algebraic varieties (Q1820905)

The Penrose transform is a tool for constructing multivalued holomorphic (outside a characteristic algebraic subvariety) solutions to the wave equation on the Minkowski space \(M^ 4\). The paper under review deals with the problem of multivaluedness of the solutions thus obtained. It is shown that f being a homogeneous meromorphic function on \({\mathbb{C}}P^ 3\), holomorphic outside an irreducible subvariety \(X\subset {\mathbb{C}}P^ 3\), its Penrose transform has the monodromy group equal to the full symmetric group.