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For questions involving Cartier and Weil divisors, the Riemann-Roch theorem and related topics (e.g. Chern classes and line bundles) on algebraic varieties.

For questions involving divisors on algebraic varieties.

The Riemann-Roch theorem states

$$\ell(D)-\ell(K-D) = \deg(D) - g + 1$$

where $D$ is a divisor, $K$ is a canonical divisor and $g$ is the genus of the surface.