algebraic variety
C18972
concept
An algebraic variety is a geometric object defined as the set of common solutions to a system of polynomial equations over a field, studied up to algebraic and topological properties.
All labels observed (16)
| Label | Occurrences |
|---|---|
| algebraic surface | 4 |
| moduli space | 4 |
| algebraic variety canonical | 3 |
| Riemann surface | 2 |
| cubic surface | 2 |
| Fano surface | 1 |
| K3 surface | 1 |
| abelian variety | 1 |
| algebraic curve representation | 1 |
| complex projective line | 1 |
| higher-dimensional algebraic variety | 1 |
| principally polarized abelian variety | 1 |
| quartic surface | 1 |
| real algebraic variety | 1 |
| singular algebraic surface | 1 |
| smooth cubic surface | 1 |
Instances (15)
| Instance | Via concept surface |
|---|---|
| Calabi–Yau manifold | — |
| Riemann sphere | Riemann surface |
| Hurwitz space | moduli space |
|
Clebsch diagonal surfaces
surface form:
Clebsch diagonal surface
|
algebraic surface |
| Whitney umbrella | singular algebraic surface |
|
Kummer surfaces
surface form:
Kummer surface
|
algebraic surface |
| Fermat surface | algebraic surface |
| Outer space (Culler–Vogtmann Outer space) | moduli space |
| Weierstrass form | algebraic curve representation |
| Shimura varieties | — |
| Seiberg–Witten curve | Riemann surface |
|
Jacobian varieties
surface form:
Jacobian variety
|
— |
| Beilinson–Drinfeld Grassmannian | moduli space |
| Teichmüller space | moduli space |
| Cayley surface | algebraic surface |