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The two families of lines on a smooth (split) quadric surface. In mathematics, a quadric or quadric hypersurface is the subspace of N-dimensional space defined by a polynomial equation of degree 2 over a field. Quadrics are fundamental examples in algebraic geometry. The theory is simplified by working in projective space rather than affine ...
In mathematics, a quadric or quadric surface is a generalization of conic sections (ellipses, parabolas, and hyperbolas). In three-dimensional space , quadrics include ellipsoids , paraboloids , and hyperboloids .
The minimal resolution of this singular surface may also be called a Kummer surface; that resolution is a K3 surface. When A is the Jacobian of a curve of genus 2, Kummer showed that the quotient A / ( ± 1 ) {\displaystyle A/(\pm 1)} can be embedded into P 3 {\displaystyle \mathbf {P} ^{3}} as a quartic surface with 16 nodes .
Labs surface, a certain septic with 99 nodes; Endrass surface, a certain surface of degree 8 with 168 nodes; Sarti surface, a certain surface of degree 12 with 600 nodes; Quotient surfaces, surfaces that are constructed as the orbit space of some other surface by the action of a finite group; examples include Kummer, Godeaux, Hopf, and Inoue ...
A hyperboloid is a quadric surface, that is, a surface defined as the zero set of a polynomial of degree two in three variables. Among quadric surfaces, a hyperboloid is characterized by not being a cone or a cylinder, having a center of symmetry, and intersecting many planes into hyperbolas.
In mathematics, especially in algebraic geometry, a quartic surface is a surface defined by an equation of degree 4. More specifically there are two closely related types of quartic surface: affine and projective. An affine quartic surface is the solution set of an equation of the form (,,) =
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