The Riemann-Roch theorem for curves
The Riemann-Roch theorem is the best general theorem for computing the Riemann-Roch space of a divisor on a curve and thus is an indispensable tool in the study of algebraic curves. In this video, we present the theorem together with a proof using cohomology theory. We also derive, as a corollary, a formula for the degree of the canonical sheaf.