Difference between revisions of "User:Richard Pinch/sandbox-WP"
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| + | =Pinch point= | ||
| + | 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> | ||
| + | |||
| + | where [4] denotes terms of degree 4 or more. | ||
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| + | ==References== | ||
| + | * {{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:
- Residually finite
- Residually nilpotent
- Residually solvable
- Residually free
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
Richard Pinch/sandbox-WP. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Richard_Pinch/sandbox-WP&oldid=30232