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In mathematics, the Riemann–Roch theorem for surfaces describes the dimension of linear systems on an algebraic surface. The classical form of it was first given by Castelnuovo (1896, 1897), after preliminary versions of it were found by Max Noether and Enriques . The sheaf-theoretic version is due to Hirzebruch.
This article incorporates material from the Citizendium article "Genus degree formula", which is licensed under the Creative Commons Attribution-ShareAlike 3.0 Unported License but not under the GFDL. Enrico Arbarello, Maurizio Cornalba, Phillip Griffiths, Joe Harris. Geometry of algebraic curves. vol 1 Springer, ISBN 0-387-90997-4, appendix A.
Abel–Jacobi theorem (algebraic geometry) Abel–Ruffini theorem (theory of equations, Galois theory) Abhyankar–Moh theorem (algebraic geometry) Absolute convergence theorem (mathematical series) Acyclic models theorem (algebraic topology) Addition theorem (algebraic geometry) Adiabatic theorem ; Ado's theorem (Lie algebra)
In the special case when k is the function field of an algebraic curve over a finite field and f is any character that is trivial on k, this recovers the geometric Riemann–Roch theorem. [ 12 ] Other versions of the arithmetic Riemann–Roch theorem make use of Arakelov theory to resemble the traditional Riemann–Roch theorem more exactly.
In mathematics, especially in algebraic geometry and the theory of complex manifolds, the adjunction formula relates the canonical bundle of a variety and a hypersurface inside that variety. It is often used to deduce facts about varieties embedded in well-behaved spaces such as projective space or to prove theorems by induction.
Algebraic geometry is a branch of mathematics which uses abstract algebraic techniques, mainly from commutative algebra, to solve geometrical problems.Classically, it studies zeros of multivariate polynomials; the modern approach generalizes this in a few different aspects.
It is an important tool in algebraic geometry, because it allows local data on algebraic varieties, in the form of modules over local rings, to be studied pointwise as vector spaces over the residue field of the ring.
Print/export Download as PDF; Printable version; In other projects ... In algebraic geometry, the projection formula states the following : [1] [2] For a morphism ...
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