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(Start article: Residual property)
(Start article: Pinch point)
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=Pinch point=
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A '''pinch point''' or '''cuspidal point''' is a type of [[Singular point of an algebraic variety|singular point]] on an [[algebraic surface]].  It is one of the three types of ordinary singularity of a surface. 
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The equation for the surface near a pinch point may be put in the form
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:<math> f(u,v,w) = u^2 - vw^2 + [4] \, </math>
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where [4] denotes terms of degree 4 or more.
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==References==
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* {{cite book | author=P. Griffiths | authorlink=Phillip Griffiths | coauthors=[[Joe Harris (mathematician)|J. Harris]] | title=Principles of Algebraic Geometry | series=Wiley Classics Library | publisher=Wiley Interscience | year=1994 | isbn=0-471-05059-8 | page=617 }}
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=Residual property=
 
=Residual property=
  

Revision as of 18:15, 25 August 2013

Pinch point

A pinch point or cuspidal point is a type of singular point on an algebraic surface. It is one of the three types of ordinary singularity of a surface.

The equation for the surface near a pinch point may be put in the form

\[ f(u,v,w) = u^2 - vw^2 + [4] \, \]

where [4] denotes terms of degree 4 or more.

References

Residual property

In the mathematical field of group theory, a group is residually X (where X is some property of groups) if it "can be recovered from groups with property X".

Formally, a group G is residually X if for every non-trivial element g there is a homomorphism h from G to a group with property X such that \(h(g)\neq e\).

More categorically, a group is residually X if it embeds into its pro-X completion (see profinite group, pro-p group), that is, the inverse limit of \(\phi\colon G \to H\) where H is a group with property X.

Examples

Important examples include:

References

Stably free module

A module which is close to being free.

Definition

A module M over a ring R is stably free if there exist free modules F and G over R such that

\[ M \oplus F = G . \, \]

Properties

  • A projective module is stably free if and only if it possesses a finite free resolution.

See also

References

How to Cite This Entry:
Richard Pinch/sandbox-WP. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Richard_Pinch/sandbox-WP&oldid=30233