In algebraic geometry, the Zariski closure of the union of the secant lines to a projective variety is the first secant variety to . It is usually denoted .
The secant variety is the Zariski closure of the union of the linear spaces spanned by collections of k+1 points on . It is usually denoted . Unless, it is always singular along, but may have other singular points.
If has dimension d, the dimension of is at most kd+d+k.
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—Ralph Waldo Emerson (18031882)