Hirzebruch–Riemann–Roch theorem
| Field | Algebraic geometry |
|---|---|
| First proof by | Friedrich Hirzebruch |
| First proof in | 1954 |
| Generalizations | Atiyah–Singer index theorem Grothendieck–Riemann–Roch theorem |
| Consequences | Riemann–Roch theorem Riemann–Roch theorem for surfaces |
In mathematics, the Hirzebruch–Riemann–Roch theorem, named after Friedrich Hirzebruch, Bernhard Riemann, and Gustav Roch, is Hirzebruch's 1954 result generalizing the classical Riemann–Roch theorem on Riemann surfaces to all complex algebraic varieties of higher dimensions. The result paved the way for the Grothendieck–Hirzebruch–Riemann–Roch theorem proved about three years later.