Namespaces
Variants
Actions

Multiple point

From Encyclopedia of Mathematics
Revision as of 17:11, 7 February 2011 by 127.0.0.1 (talk) (Importing text file)
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)
Jump to: navigation, search

of a planar curve

A singular point at which the partial derivatives of order up to and including vanish, but where at least one partial derivative of order does not vanish. For example, if , , does not vanish, the multiple point is called a double point; if the first and second partial derivatives vanish at , but at least one third derivative does not, the multiple point is called a triple point; etc.


Comments

References

[a1] J.L. Coolidge, "Algebraic plane curves" , Dover, reprint (1959)
[a2] D. Hilbert, S.E. Cohn-Vossen, "Geometry and the imagination" , Chelsea (1952) pp. 173 (Translated from German)
[a3] P.A. Griffiths, J.E. Harris, "Principles of algebraic geometry" , Wiley (Interscience) (1978)
[a4] W. Fulton, "Algebraic curves" , Benjamin (1969) pp. 66
How to Cite This Entry:
Multiple point. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Multiple_point&oldid=23906
This article was adapted from an original article by A.B. Ivanov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article