nLab Hirzebruch-Riemann-Roch theorem

Idea

The Hirzebruch-Riemann-Roch theorem identifies for a holomorphic vector bundle $E$ the alternating sum of its abelian sheaf cohomology groups (hence for trivial bundle the index of the Dolbeault operator) with the Chern character of the bundle cupped with the Todd class of the underlying complex manifold.

Related concepts

• Atiyah-Singer index theorem

• Grothendieck-Riemann-Roch theorem

• Todd genus, geometric quantization

References

• Wikipedia: Hirzebruch-Riemann-Roch theorem

• Friedrich Hirzebruch: Topological methods in algebraic geometry, Springer (1978), Classics in Mathematics, Springer (1995) [doi:10.1007/978-3-642-62018-8, pdf]

Review of the genesis of the theorem:

• Dieter Kotschick: 1953, The Institute Letter, IAS (2013) [online]