#degree_of_an_algebraic_variety
Degree of an algebraic variety
Number used in algebraic geometry
In mathematics, the degree of an affine or projective variety of dimension n is the number of intersection points of the variety with n hyperplanes in general position. For an algebraic set, the intersection points must be counted with their intersection multiplicity, because of the possibility of multiple components. For (irreducible) varieties, if one takes into account the multiplicities and, in the affine case, the points at infinity, the hypothesis of general position may be replaced by the much weaker condition that the intersection of the variety has the dimension zero. This is a generalization of Bézout's theorem.
Tue 10th
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