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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“In different hours, a man represents each of several of his ancestors, as if there were seven or eight of us rolled up in each man’s skin,—seven or eight ancestors at least, and they constitute the variety of notes for that new piece of music which his life is.”
—Ralph Waldo Emerson (1803–1882)