Category:Algebraic geometry

Algebraic geometry is a branch of mathematics which, as the name suggests, combines abstract algebra, especially commutative algebra, with geometry. It can be seen as the study of solution sets of systems of algebraic equations. When there is more than one variable, geometric considerations enter, and are important to understand the phenomenon. One can say that the subject starts where equation solving leaves off, and it becomes at least as important to understand the totality of solutions of a system of equations as to find some solution; this does lead into some of the deepest waters in the whole of mathematics, both conceptually and in terms of technique.

Subcategories

There are 9 subcategories to this category.

Algebraic curves Algebraic groups Algebraic surfaces

A Algebraic varieties D Diophantine geometry I Invariant theory M Modular forms

P Projective geometry S Surfaces

Articles in category "Algebraic geometry"

There are 94 articles in this category.

Algebraic geometry A Abelian variety Addition theorem Algebraic curve Algebraic form Algebraic geometry and analytic geometry Algebraic group Algebraic stack Algebraic surface Algebraic variety Analytic geometry Analytic variety Arithmetic group Arithmetic of abelian varieties B Brill-Noether theory C Calabi-Yau manifold Codimension Cohen-Macaulay ring Coherent sheaf Complete algebraic variety Complex multiplication Complex projective space Conifold Crystal (mathematics) Cubic surface D Deformation theory Del Pezzo surface Deligne conjecture Descent (category theory) Dessin d'enfant Differential of the first kind

D cont. Dimension of an algebraic variety Divisor (algebraic geometry) E Elimination theory Étale cohomology F Flag manifold Flasque sheaf Flat module Function field G Generalized Riemann hypothesis Geometric invariant theory Glossary of scheme theory Grassmannian Grothendieck's Galois theory Grothendieck's Séminaire de géométrie algébrique Grothendieck-Riemann-Roch theorem H Hasse-Weil zeta function Hilbert's Nullstellensatz Hodge conjecture Hodge cycle Hodge index theorem Homological algebra Homotopical algebra Hyperelliptic curve I Intersection cohomology Intersection number Invertible sheaf Italian school of algebraic geometry J Jacobian conjecture K Kähler differential Kähler manifold L Linear system of divisors List of algebraic geometry topics

L cont. Locally ringed space M Modular equation Moduli space Motive (algebraic geometry) Motivic cohomology P Plücker coordinates Q Quasiprojective variety R Rational function Regular function Regular local ring Riemann-Roch theorem S Sato-Tate conjecture Scheme (mathematics) Segre embedding Serre duality Serre's multiplicity conjectures Severi-Brauer variety Sheaf Sheaf cohomology Sheaf spanned by global sections Singular point of an algebraic variety Singularity theory Spectrum of a ring Stack (category theory) Steiner surface T Tangent half-angle formula Toric geometry V Valuation (mathematics) W Weil conjectures Z Zariski tangent space Zariski topology