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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 :.
Fyodor L. Zak (Russian: Федор Лазаревич Зак (born December 2, 1949, in Moscow) is a Russian mathematician working on mathematical economics and algebraic geometry [1] who classified the Scorza varieties. [2]
The word secant comes from the Latin word secare, meaning to cut. [2] In the case of a circle, a secant intersects the circle at exactly two points. A chord is the line segment determined by the two points, that is, the interval on the secant whose ends are the two points. [3]
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 ...
Jensen's inequality generalizes the statement that a secant line of a convex function lies above its graph. Visualizing convexity and Jensen's inequality. In mathematics, Jensen's inequality, named after the Danish mathematician Johan Jensen, relates the value of a convex function of an integral to the integral of the convex function.
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.
Defense Secretary Pete Hegseth ordered an immediate pause on gender-affirming medical care procedures for all active-duty service members in a memo that was addressed to senior Pentagon leadership ...
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})} .