TRANSVERSELY PROJECTIVE FOLIATIONS ON SURFACES: EXISTENCE OF MINIMAL FORM AND PRESCRIPTION OF MONODROMY

Source abstract

We introduce a notion of minimal form for transversely projective structures of singular foliations on complex manifolds. Our first main result says that this minimal form exists and is unique when ambient space is two-dimensional. From this result, one obtains a natural way to produce invariants for transversely projective foliations on surfaces. Our second main result says that on projective surfaces one can construct singular transversely projective foliations with prescribed monodromy.