Definition & Betydelse | Engelska ordet CODIMENSION

Definition av CODIMENSION

1. (matematik) skillnaden i dimension mellan ett rum och ett däri givet underrum

Exempel på hur du använder CODIMENSION i en mening

• In particular, they solve the anisotropic Plateau problem in arbitrary dimension and codimension for any collection of rectifiable sets satisfying a combination of general homological, cohomological or homotopical spanning conditions.
• The only intersection number that can be calculated directly from the definition is the intersection of hypersurfaces (subvarieties of X of codimension one) that are in general position at x.
• In geometric terms, ramification is something that happens in codimension two (like knot theory, and monodromy); since real codimension two is complex codimension one, the local complex example sets the pattern for higher-dimensional complex manifolds.
• that it be tangent to a codimension one foliation on the manifold, whose equivalence is the content of the Frobenius theorem.
• The unmixed theorem applies in particular to the zero ideal (an ideal generated by zero elements) and thus it says a Cohen–Macaulay ring is an equidimensional ring; in fact, in the strong sense: there is no embedded component and each component has the same codimension.
• There is also a structure theorem for Gorenstein rings of codimension 3 in terms of the Pfaffians of a skew-symmetric matrix, by Buchsbaum and Eisenbud.
• In mathematics, codimension is a basic geometric idea that applies to subspaces in vector spaces, to submanifolds in manifolds, and suitable subsets of algebraic varieties.
• Roughly, the Whitney trick allows one to "unknot" knotted spheres – more precisely, remove self-intersections of immersions; it does this via a homotopy of a disk – the disk has 2 dimensions, and the homotopy adds 1 more – and thus in codimension greater than 2, this can be done without intersecting itself; hence embeddings in codimension greater than 2 can be understood by surgery.
• If the foliated manifold has non-empty tangential boundary, then a codimension 1 foliation is taut if every leaf meets a transverse circle or a transverse arc with endpoints on the tangential boundary.
• Saddle-node bifurcations and Hopf bifurcations are the only generic local bifurcations which are really codimension-one (the others all having higher codimension).
• Any two distinct null geodesic hypersurfaces of codimension 1 which intersect at more than just a point in AdS divides AdS into four distinct regions, two of which are spacelike.
• The notion of a CR structure attempts to describe intrinsically the property of being a hypersurface (or certain real submanifolds of higher codimension) in complex space by studying the properties of holomorphic vector fields which are tangent to the hypersurface.
• If an intersection is transverse, then the intersection will be a submanifold whose codimension is equal to the sums of the codimensions of the two manifolds.
• In mathematics, the Fulton–Hansen connectedness theorem is a result from intersection theory in algebraic geometry, for the case of subvarieties of projective space with codimension large enough to make the intersection have components of dimension at least 1.
• The theorem can also be extended, beyond the context of hypersurfaces, to the theory of submanifolds of arbitrary codimension.
• Geometrically this corresponds to intersection, where two n/2-dimensional submanifolds in an n-dimensional manifold generically intersect in a 0-dimensional submanifold (a set of points), by adding codimension.
• More abstractly, the codimension of a map is the dimension of the cokernel, while the relative dimension of a map is the dimension of the kernel.
• Then on the edges of this octant (singularities of codimension 2) the curvature is nonpositive (because of branching geodesics), yet it is not the case at the origin (singularity of codimension 3), where a triangle such as (0,0,e), (0,e,0), (e,0,0) has a median longer than would be in the Euclidean plane, which is characteristic of nonnegative curvature.
• For example, ramification is a phenomenon of codimension 1 (in the geometry of complex manifolds, reflecting as for Riemann surfaces that ramify at single points that it happens in real codimension two).
• Abrosimov proved that holomorphic automorphisms of a quadric of codimension two are furnished by birational transformations of degree two.

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