Multiple point
From HandWiki
of a planar curve $F(x,y)=0$
A singular point at which the partial derivatives of order up to and including $n$ vanish, but where at least one partial derivative of order $n+1$ does not vanish. For example, if $F(x_0,y_0)=0$, $F_x'(x_0,y_0)=0$, $F_{yy}(x_0,y_0)$ does not vanish, the multiple point $M(x_0,y_0)$ is called a double point; if the first and second partial derivatives vanish at $M(x_0,y_0)$, but at least one third derivative does not, the multiple point is called a triple point; etc.
References
| [a1] | J.L. Coolidge, "Algebraic plane curves" , Dover, reprint (1959) MR0120551 Template:ZBL |
| [a2] | D. Hilbert, S.E. Cohn-Vossen, "Geometry and the imagination" , Chelsea (1952) pp. 173 (Translated from German) MR0046650 Template:ZBL |
| [a3] | P.A. Griffiths, J.E. Harris, "Principles of algebraic geometry" , Wiley (Interscience) (1978) MR0507725 Template:ZBL |
| [a4] | W. Fulton, "Algebraic curves" , Benjamin (1969) pp. 66 MR0313252 MR0260752 Template:ZBL Template:ZBL |
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