The Hirzebruch-Riemann-Roch Theorem is a fundamental result in algebraic geometry that provides a formula for calculating the Euler characteristic of coherent sheaves on smooth projective varieties. It connects the geometry of a variety with its topology and cohomological properties, allowing for the computation of dimensions of spaces of global sections of sheaves. This theorem extends the classical Riemann-Roch theorem for curves to higher dimensions, thus playing a pivotal role in the understanding of Riemann surfaces and their generalizations.
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