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2. Hypersurface - Wikipedia

   en.wikipedia.org/wiki/Hypersurface

   In geometry, a hypersurface is a generalization of the concepts of hyperplane, plane curve, and surface. A hypersurface is a manifold or an algebraic variety of dimension n − 1 , which is embedded in an ambient space of dimension n , generally a Euclidean space , an affine space or a projective space . [ 1 ]

3. Fano variety - Wikipedia

   en.wikipedia.org/wiki/Fano_variety

   The adjunction formula implies that K D = (K X + D)| D = (−(n+1)H + deg(D)H)| D, where H is the class of a hyperplane. The hypersurface D is therefore Fano if and only if deg(D) < n+1. More generally, a smooth complete intersection of hypersurfaces in n-dimensional projective space is Fano if and only if the sum of their degrees is at most n.

4. Hyperbolic coordinates - Wikipedia

   en.wikipedia.org/wiki/Hyperbolic_coordinates

   In special relativity the focus is on the 3-dimensional hypersurface in the future of spacetime where various velocities arrive after a given proper time. Scott Walter [ 2 ] explains that in November 1907 Hermann Minkowski alluded to a well-known three-dimensional hyperbolic geometry while speaking to the Göttingen Mathematical Society, but ...

5. Quadric (algebraic geometry) - Wikipedia

   en.wikipedia.org/wiki/Quadric_(algebraic_geometry)

   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 space. An example is the quadric surface =

6. Adjunction formula - Wikipedia

   en.wikipedia.org/wiki/Adjunction_formula

   In mathematics, especially in algebraic geometry and the theory of complex manifolds, the adjunction formula relates the canonical bundle of a variety and a hypersurface inside that variety. It is often used to deduce facts about varieties embedded in well-behaved spaces such as projective space or to prove theorems by induction.

7. Hyperbolic manifold - Wikipedia

   en.wikipedia.org/wiki/Hyperbolic_manifold

   For > the hyperbolic structure on a finite volume hyperbolic -manifold is unique by Mostow rigidity and so geometric invariants are in fact topological invariants. One of these geometric invariants used as a topological invariant is the hyperbolic volume of a knot or link complement, which can allow us to distinguish two knots from each other ...