for the tangent bundle of one obtains Computations of the Todd class For any algebraic curve the Todd class is just . Since is projective, it can be embedded into some and we can find using the normal sequenceand properties of chern classes. For example, if we have a degree plane curve in , we find the total chern class iswhere is the hyperplane class in restricted to . Hirzebruch-Riemann-Roch formula For any coherent sheaf F on a smooth compact complex manifold M, one has where is its holomorphic Euler characteristic, and its Chern character. See also Genus of a multiplicative sequence Notes References Friedrich Hirzebruch, Topological methods in algebraic geometry, Springer (1978) Characteristic classes