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.

Try in SPARQL

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

Description generation (CDg)

The one-sentence description above was generated by prompting gpt-5.1 with the class name and this instruction.

Instruction

generate a one-sentence description for a given conceptual class.
# Response Format
Return only the sentence: "Description: [one-sentence description of the conceptional class]"

Input

Class: algebraic variety

Generated description

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.

Instances (15)

Instance	Via concept surface
Calabi–Yau manifold	—
Riemann sphere	Riemann surface
Hurwitz space	moduli space
Clebsch diagonal surface linked to: Clebsch diagonal surfaces	algebraic surface
Whitney umbrella	singular algebraic surface
Kummer surface linked to: Kummer surfaces	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 variety linked to: Jacobian varieties	—
Beilinson–Drinfeld Grassmannian	moduli space
Teichmüller space	moduli space
Cayley surface	algebraic surface