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.
Observed surface forms (15)
- algebraic surface ×4
- moduli space ×4
- 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)
- Calabi–Yau manifold
- Riemann sphere via concept surface "Riemann surface"
- Hurwitz space via concept surface "moduli space"
-
Clebsch diagonal surfaces
via concept surface "algebraic surface"
surface form: Clebsch diagonal surface
- Whitney umbrella via concept surface "singular algebraic surface"
-
Kummer surfaces
via concept surface "algebraic surface"
surface form: Kummer surface
- Fermat surface via concept surface "algebraic surface"
- Outer space (Culler–Vogtmann Outer space) via concept surface "moduli space"
- Weierstrass form via concept surface "algebraic curve representation"
- Shimura varieties
- Seiberg–Witten curve via concept surface "Riemann surface"
-
Jacobian varieties
surface form: Jacobian variety
- Beilinson–Drinfeld Grassmannian via concept surface "moduli space"
- Teichmüller space via concept surface "moduli space"
- Cayley surface via concept surface "algebraic surface"