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 Ch*(F) its Chern character.
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“Ideals possess the strange quality that if they were completely realized they would turn into nonsense. One could easily follow a commandment such as “Thou shalt not kill” to the point of dying of starvation; and I might establish the formula that for the proper functioning of the mesh of our ideals, as in the case of a strainer, the holes are just as important as the mesh.”
—Robert Musil (1880–1942)