Holomorphic Sections of Line Bundles on the Jet Spaces of the Riemann Sphere

Abstract

Fix a point t0 in the circle S1. The space Jk (t0, ℙ1) of k-jets at t0 of C∞ maps from S1 to the Riemann sphere ℙ1 is a k + 1 dimensional complex algebraic manifold. We identify a class of holomorphic sections of line bundles on Jk (t0, ℙ1).