For a compact Riemann surface X of genus g and a divisor D: ℓ(D) − ℓ(K − D) = deg D + 1 − g, where K is the canonical divisor. Extends to algebraic curves/varieties and Grothendieck's K-theoretic version.
For a compact Riemann surface X of genus g and a divisor D: ℓ(D) − ℓ(K − D) = deg D + 1 − g, where K is the canonical divisor. Extends to algebraic curves/varieties and Grothendieck's K-theoretic version.