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A secant variety can be used to show the fact that a smooth projective curve can be embedded into the projective 3-space as follows. [2] Let be a smooth curve. Since the dimension of the secant variety S to C has dimension at most 3, if >, then there is a point p on that is not on S and so we have the projection from p to a hyperplane H, which gives the embedding :.
The twisted cubic is a projective algebraic variety. Algebraic varieties are the central objects of study in algebraic geometry, a sub-field of mathematics. Classically, an algebraic variety is defined as the set of solutions of a system of polynomial equations over the real or complex numbers. Modern definitions generalize this concept in ...
The union of the tangent and secant lines (the secant variety) of a twisted cubic C fill up P 3 and the lines are pairwise disjoint, except at points of the curve itself. In fact, the union of the tangent and secant lines of any non-planar smooth algebraic curve is three-dimensional.
The secant variety to a projective variety is the closure of the union of all secant lines to V in . section ring The section ring or the ring of sections of a line bundle L on a scheme X is the graded ring ⊕ 0 ∞ Γ ( X , L n ) {\displaystyle \oplus _{0}^{\infty }\Gamma (X,L^{n})} .
secant 1. A line intersecting a variety in 2 points, or more generally an n-dimensional projective space meeting a variety in n+1 points. 2. A secant variety is the union of the secants of a variety. second kind All residues at poles are zero secundum An intersection of two primes (hyperplanes) in projective space. (Semple & Roth 1949, p.2 ...
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