KnowraRiemann–Roch theoremLinked fromLinked fromThe 14 pages that link to Riemann–Roch theorem, each with the reason it gives.All 14Broader topic 3Related 9Narrower topic 1Compared with 1Bernhard RiemannBroader topic: Riemann’s work on surfaces and complex functions led to this foundational result, later generalized by Roch.Riemann surfaceRelated: It constrains which functions and differentials can exist on a surface of given genus.Algebraic curveRelated: It turns curve geometry into precise counts of functions with prescribed poles.Sheaf cohomologyRelated: Sheaf cohomology supplies the dimensions and correction terms appearing in its modern formulations.Mittag-Leffler theoremCompared with: Unlike the plane theorem, it quantifies finite-dimensional restrictions on compact surfaces.Atiyah–Singer index theoremRelated: Its higher-dimensional descendants arise from index formulas for complex differential operators.Hirzebruch–Riemann–Roch theoremBroader topic: Hirzebruch’s formula extends this dimension-counting principle to higher dimensions.Grothendieck–Riemann–Roch theoremNarrower topic: The classical curve theorem is the formula that this result extends.Abel’s theoremRelated: Together with Abel’s theorem, it gives a central description of divisors and functions on curves.Cayley–Bacharach theoremRelated: Duality and dimension counts on curves provide a broader framework for interpolation dependencies.Riemann–Roch theorem for surfacesBroader topic: The surface theorem extends this divisor-counting principle by adding intersection terms.Birkhoff–Grothendieck theoremRelated: It helps control sections and degrees when proving the splitting on the genus-zero curve.Clifford's theorem on special divisorsRelated: Its formula turns the specialness condition into the numerical bound.Green's conjectureRelated: It underlies the dimension counts used to define curve invariants in the conjecture.