In
algebraic geometry, given irreducible subvarieties ''V'', ''W'' of a
projective space P
''n'', the ruled join of ''V'' and ''W'' is the union of all lines from ''V'' to ''W'' in P
2''n''+1, where ''V'', ''W'' are embedded into P
2''n''+1 so that the last (resp. first) ''n'' + 1 coordinates on ''V'' (resp. ''W'') vanish.
It is denoted by ''J''(''V'', ''W''). For example, if ''V'' and ''W'' are linear subspaces, then their join is the
linear span
In mathematics, the linear span (also called the linear hull or just span) of a set of vectors (from a vector space), denoted , pp. 29-30, ยงยง 2.5, 2.8 is defined as the set of all linear combinations of the vectors in . It can be characteri ...
of them, the smallest linear subcontaining them.
The join of several subvarieties is defined in a similar way.
See also
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Secant variety In algebraic geometry, the secant variety \operatorname(V), or the variety of chords, of a projective variety V \subset \mathbb^r is the Zariski closure of the union of all secant lines (chords) to ''V'' in \mathbb^r:
:\operatorname(V) = \bigcup_ ...
References
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{{algebraic-geometry-stub
Algebraic geometry