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Reiss relation : ウィキペディア英語版
Reiss relation
In algebraic geometry, the Reiss relation, introduced by , is a condition on the second-order elements of the points of a plane algebraic curve meeting a given line.
==Statement==

If ''C'' is a complex plane curve given by the zeros of a polynomial ''f''(''x'',''y'') of two variables, and ''L'' is a line meeting ''C'' transversely and not meeting ''C'' at infinity, then
:\sum\fracf_xf_y+f_f_x^2}=0
where the sum is over the points of intersection of ''C'' and ''L'', and ''f''''x'', ''f''''xy'' and so on stand for partial derivatives of ''f'' .
This can also be written as
:\sum\frac=0
where κ is the curvature of the curve ''C'' and θ is the angle its tangent line makes with ''L'', and the sum is again over the points of intersection of ''C'' and ''L'' .

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