The Riemann-Roch theorem for algebraic manifolds

Abstract

In this chapter V is a complex n-dimensional manifold. The proof of the Riemann-Roch theorem depends on results on compact complex manifolds which are due to Cartan, Dolbeault, Kodaira, Serre and Spencer. These results are summarised in § 15. At two points in the proof it becomes necessary to make additional assumptions on V: first that V is a Kähler manifold (15.6–15.9) and then that V is algebraic.