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jumping line
In mathematics, a jumping line or exceptional line of a vector bundle over projective space is a projective line in projective space where the vector bundle has exceptional behavior, in other words the structure of its restriction to the line "jumps". Jumping lines were introduced by . The jumping lines of a vector bundle form a proper closed subset of the Grassmannian of all lines of projective space.
The Birkhoff–Grothendieck theorem classifies the ''n''-dimensional vector bundles over a projective line as corresponding to unordered ''n''-tupes of integers.
==Example==
Suppose that ''V'' is a 4-dimensional complex vector space with a non-degenerate skew-symmetric form. There is a rank 2 vector bundle over the 3-dimensional complex projective space associated to ''V'', that assigns to each line ''L'' of ''V'' the 2-dimensional vector space ''L''⊥/''L''. Then a plane of ''V'' corresponds to a jumping line of this vector bundle if and only if it is isotropic for the skew-symmetric form.
抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』
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