Riemann Roch space and motivating cohomology

The Riemann-Roch space is an extremely useful tool in algebraic geometry as it is used to generate morphisms. In this video, we introduce it via global sections of a sheaf and see how it is useful in a simple example giving a criterion for a smooth curve to be isomorphic to the projective line. We next consider the problem of lifting sections, a subtlety in the study of the Riemann-Roch space, that crops up when trying to construct morphisms using it. Addressing this problem requires cohomology, the theme of this playlist.