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In algebraic geometry, the secant variety … In algebraic geometry, the secant variety , or the variety of chords, of a projective variety is the Zariski closure of the union of all secant lines (chords) to V in : (for , the line is the tangent line.) It is also the image under the projection of the closure Z of the . Note that Z has dimension and so has dimension at most . More generally, the secant variety is the Zariski closure of the union of the linear spaces spanned by collections of k+1 points on . It may be denoted by . The above secant variety is the first secant variety. Unless , it is always singular along , but may have other singular points. If has dimension d, the dimension of is at most .A useful tool for computing the dimension of a secant variety is .ing the dimension of a secant variety is .
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| rdfs:comment |
In algebraic geometry, the secant variety … In algebraic geometry, the secant variety , or the variety of chords, of a projective variety is the Zariski closure of the union of all secant lines (chords) to V in : (for , the line is the tangent line.) It is also the image under the projection of the closure Z of the . Note that Z has dimension and so has dimension at most . If has dimension d, the dimension of is at most .A useful tool for computing the dimension of a secant variety is .ing the dimension of a secant variety is .
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| rdfs:label |
Secant variety
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