Science Fair Project Encyclopedia
List of algebraic geometry topics
This is a list of algebraic geometry topics, by Wikipedia page.
| Contents |
Classical topics in projective geometry
- Affine space
- Projective space
- Projective line, cross-ratio
- Projective plane
- Complex projective space
- Plane at infinity, hyperplane at infinity
- Projective frame
- Projective transformation
- Fundamental theorem of projective geometry
- Duality (projective geometry)
- Real projective plane
- Real projective space
- Segre embedding, multi-way projective space
Algebraic curves
- Conics, Pascal's theorem, Brianchon's theorem
- Elliptic curve, cubic curve
- Hyperelliptic curve
- Klein quartic
- modular curve
- Fermat curve
- Bézout's theorem
- Brill-Noether theory
- Genus (mathematics)
- Riemann surface
- Riemann-Hurwitz formula
- Riemann-Roch theorem
- Abelian integral
- Differential of the first kind
- Jacobian variety
- Hurwitz's automorphisms theorem
Algebraic surfaces
Algebraic geometry: classical approach
- Algebraic variety
- Tangent space, Zariski tangent space
- Function field
- Ample vector bundle
- Linear system of divisors
- Birational geometry
- Intersection number
- Intersection theory
- Serre's multiplicity conjectures
- Modular form
- Moduli space
- Modular equation
- Algebraic function
- Algebraic form
- Addition theorem
- Invariant theory
- Geometric invariant theory
- Toric geometry
- Deformation theory
- Singular point, non-singular
- Singularity theory
- Weil conjectures
Complex manifolds
- Kähler manifold
- Calabi-Yau manifold
- Stein manifold
- Hodge theory
- Hodge cycle
- Hodge conjecture
- Algebraic geometry and analytic geometry
- Mirror symmetry
Algebraic groups
- Identity component
- Linear algebraic group
- Abelian variety
- Grassmannian
- Flag manifold
- Algebraic torus
- Weil restriction
- Differential Galois theory
Contemporary foundations
Main article glossary of scheme theory
Commutative algebra
- Prime ideal
- Valuation (mathematics)
- Regular local ring
- Regular sequence (algebra)
- Cohen-Macaulay ring
- Gorenstein ring
- Koszul complex
- Spectrum of a ring
- Zariski topology
- Kähler differential
Sheaf theory
- Locally ringed space
- Coherent sheaf
- Invertible sheaf
- Sheaf cohomology
- Grothendieck-Riemann-Roch theorem
Schemes
- Affine scheme
- Scheme
- Glossary of scheme theory
- Éléments de géométrie algébrique
- Grothendieck's Séminaire de géométrie algébrique
- Flat morphism
- Group scheme
- Semistable elliptic curve
Category theory
- Grothendieck topology
- Topos
- Descent (category theory)
- Algebraic stack
- Gerbe
- Etale cohomology
- Motive (mathematics)
- Motivic cohomology
- Homotopical algebra
The geometers
- Niels Henrik Abel
- Carl Gustav Jakob Jacobi
- Jakob Steiner
- Julius Plücker
- Bernhard Riemann
- William Kingdon Clifford
- Italian school of algebraic geometry
- Solomon Lefschetz
- Oscar Zariski
- Erich Kähler
- W. V. D. Hodge
- André Weil
- Jean-Pierre Serre
- Alexander Grothendieck
- Igor Shafarevich
- Heisuke Hironaka
- Shigefumi Mori
- Vladimir Voevodsky
03-10-2013 05:06:04
The contents of this article is licensed from www.wikipedia.org under the GNU Free Documentation License. Click here to see the transparent copy and copyright details
The contents of this article is licensed from www.wikipedia.org under the GNU Free Documentation License. Click here to see the transparent copy and copyright details