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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. 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 =

4. List of formulas in elementary geometry - Wikipedia

   en.wikipedia.org/wiki/List_of_formulas_in...

   The basic quantities describing a sphere (meaning a 2-sphere, a 2-dimensional surface inside 3-dimensional space) will be denoted by the following variables r {\displaystyle r} is the radius, C = 2 π r {\displaystyle C=2\pi r} is the circumference (the length of any one of its great circles ),

5. Quadric - Wikipedia

   en.wikipedia.org/wiki/Quadric

   In mathematics, a quadric or quadric surface (quadric hypersurface in higher dimensions), is a generalization of conic sections (ellipses, parabolas, and hyperbolas).It is a hypersurface (of dimension D) in a (D + 1)-dimensional space, and it is defined as the zero set of an irreducible polynomial of degree two in D + 1 variables; for example, D = 1 in the case of conic sections.

6. Adjunction formula - Wikipedia

   en.wikipedia.org/wiki/Adjunction_formula

   Consequently, the adjunction formula says that the restriction of (d − 3)H to C equals the canonical class of C. This restriction is the same as the intersection product (d − 3)H ⋅ dH restricted to C, and so the degree of the canonical class of C is d(d−3). By the Riemann–Roch theorem, g − 1 = (d−3)d − g + 1, which implies the ...

7. Quintic threefold - Wikipedia

   en.wikipedia.org/wiki/Quintic_threefold

   One of the easiest examples to check of a Calabi-Yau manifold is given by the Fermat quintic threefold, which is defined by the vanishing locus of the polynomial = + + + + Computing the partial derivatives of gives the four polynomials = = = = = Since the only points where they vanish is given by the coordinate axes in , the vanishing locus is empty since [::::] is not a point in .