# Holomorphic Morse Inequalities

Abstract: Given a holomorphic vector field V on a compact complex manifold M, the Atiyah-Bott holomorphic Lefschetz formula expresses the Chern numbers of M in terms of the zeros of V. In this article, it is shown that if M is a Kahler manifold and V generates an isometry of M, the holomorphic Lefschetz formula can be generalized to a system of Inequalities, analogous to the Morse inequalities for real manifolds. (link to pdf)