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degree of an algebraic variety
The degree of an algebraic variety in mathematics is defined, for a projective variety ''V'', by an elementary use of intersection theory.
==Definition==
For ''V'' embedded in a projective space ''P''''n'' and defined over some algebraically closed field ''K'', the degree ''d'' of ''V'' is the number of points of intersection of ''V'', defined over ''K'', with a linear subspace ''L'' in general position, when
:
Here dim(''V'') is the dimension of ''V'', and the codimension of ''L'' will be equal to that dimension. The degree ''d'' is an extrinsic quantity, and not intrinsic as a property of ''V''. For example the projective line has an (essentially unique) embedding of degree ''n'' in ''P''''n''.
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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