Category
page 1Theorems in algebraic geometry
modularity theorem
theorem in mathematics
Hilbert's Nullstellensatz
Theorem: polynomials without common complex zeros generate the unit ideal
Bézout's theorem
theorem calculating the number of intersection points of two algebraic curves in terms of their degrees
Faltings' theorem
theorem
Riemann–Roch theorem
theorem that the Euler characteristic of the sheaf cohomology of a holomorphic line bundle on a Riemann surface equals the degree of the bundle plus half of the Euler characteristic of the surface
Lüroth's theorem
subfield of K(X) is isomorphic to K(X)
Cayley–Bacharach theorem
statement about cubic curves in the projective plane
Ribet's theorem
Result concerning properties of Galois representations associated with modular forms
Hirzebruch–Riemann–Roch theorem
on the Euler characteristic of a holomorphic vector bundle on a compact complex manifold
Grothendieck–Hirzebruch–Riemann–Roch theorem
Result in algebraic geometry
Birkhoff–Grothendieck theorem
classifies holomorphic vector bundles over the complex projective line
Belyi's theorem
connects non-singular algebraic curves with compact Riemann surfaces
Lefschetz hyperplane theorem
theorem that the inclusion between a projective variety and its hyperplane section induces isomorphisms of homology, cohomology or homotopy groups in low degrees
Harnack's curve theorem
number of connected components an algebraic curve can have
Kodaira embedding theorem
characterises non-singular projective varieties amongst compact Kähler manifolds
Riemann–Roch theorem for surfaces
Mathematical theorem