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I believe you meant "Hirzebruch-Riemann-Roch Theorem". Here's a wiki-style article:

The Hirzebruch-Riemann-Roch Theorem is a foundational result in algebraic geometry, first proved by Friedrich Hirzebruch in 1962. It is a generalization of the celebrated Riemann-Roch Theorem, which describes the relationship between complex algebraic curves. The Hirzebruch-Riemann-Roch Theorem extends this result to higher-dimensional algebraic geometry, providing a profound understanding of the structure of compact complex manifolds.

The theorem relates the holomorphic Euler characteristic of a complex manifold X, denoted ch(X), to the holomorphic Euler characteristic of its determinant line bundle, denoted ∫(ch(D(X))). Here, D(X) is the determinant line bundle of X, which is a fundamental object in algebraic geometry. The theorem states that the holomorphic Euler characteristic of a complex manifold factorizes into the Euler characteristic of its determinant line bundle and the Euler characteristic of its underlying manifold.

The Hirzebruch-Riemann-Roch Theorem has had a profound impact on many areas of mathematics, including algebraic geometry, number theory, and theoretical physics. It has been used to solve numerous problems in algebraic geometry, such as the classification of algebraic surfaces and the study of Calabi-Yau manifolds. Furthermore, it has been generalized to more general settings, including higher-dimensional complex manifolds and symplectic geometry.

The proof of the Hirzebruch-Riemann-Roch Theorem relied heavily on deep insights into the topology of complex manifolds, as well as the development of new tools and techniques in algebraic geometry. It is considered a cornerstone of modern algebraic geometry and continues to play an active role in shaping the field.