Example image of eyePlorer eyePlorer map for 'Algebraic curve': Algebraic geometry Algebraic variety Dimension of an algebraic variety Circle Conic section Curve Hyperelliptic curve Projective space Fermat curve Homogeneous polynomial Irreducible component Birational geometry Equivalence of categories Function field of an algebraic variety Algebraically closed field Compact space Connected space Manifold Orientability Riemann surface Singular point of a curve Tangent space Jacobian matrix and determinant Rank (linear algebra) Geometric genus Genus (mathematics) Rational normal curve List of curves Cubic plane curve Elliptic curve Rational point Abelian group Collinearity Elliptic function Fundamental pair of periods Faltings' theorem Hyperbolic geometry Klein quartic Function field (scheme theory) Claude Chevalley George Salmon Jean-Pierre Serre John Milnor Phillip Griffiths Robin Hartshorne Abel–Jacobi map AF+BG theorem Ampersand curve Beauville–Laszlo theorem Belyi's theorem