In algebraic geometry, a closed immersion of schemes is a regular embedding of codimension r if each point x in X has an open affine neighborhood U in Y such that the ideal of is generated by a regular sequence of length r. A regular embedding of codimension one is precisely an effective Cartier divisor.
immersion i : X ↪ Y {\displaystyle i:X\hookrightarrow Y} of schemes is a regularembedding of codimension r if each point x in X has an open affine neighborhood...
R with respect to I. If Y is the product X × X and the embedding i is the diagonal embedding, then the normal bundle to X in Y is the tangent bundle...
presentation is the open immersion of an open closed subscheme. Segre embeddingRegularembedding Mumford, The Red Book of Varieties and Schemes, Section II.5...
embedding, cellular embedding or map is an embedding in which every face is homeomorphic to an open disk. A closed 2-cell embedding is an embedding in...
W^{\ell ,q}(\mathbf {R} ^{n})} and the embedding is continuous. In the special case of k = 1 and ℓ = 0, Sobolev embedding gives W 1 , p ( R n ) ⊆ L p ∗ ( R...
polynomial function of algebraic varieties a regular map (graph theory), a symmetric 2-cell embedding of a graph into a closed surface This disambiguation...
intersection.) A generalization to a situation where the assumption on regularembedding is weakened is due to Kleiman (1981). The following definition is...
planar graph. A 1-outerplanar embedding of a graph is the same as an outerplanar embedding. For k > 1 a planar embedding is k-outerplanar if removing the...
multiplication being the tensor product. Plücker embedding The Plücker embedding is the closed embedding of the Grassmannian variety into a projective space...
An embedded submanifold (also called a regular submanifold), is an immersed submanifold for which the inclusion map is a topological embedding. That...
<\theta } , say that an elementary embedding j : M → H ( θ ) {\displaystyle j:M\to H(\theta )} a small embedding if M {\displaystyle M} is transitive...
A regular dodecahedron or pentagonal dodecahedron is a dodecahedron that is regular, which is composed of 12 regular pentagonal faces, three meeting at...
The universal embedding theorem, or Krasner–Kaloujnine universal embedding theorem, is a theorem from the mathematical discipline of group theory first...
graph is a graph whose drawing, embedded in some Euclidean space R n {\displaystyle \mathbb {R} ^{n}} , forms a regular tiling. This implies that the group...
same regular homotopy class if there exists a regular homotopy between them. Regular homotopy for immersions is similar to isotopy of embeddings: they...
Perl Compatible Regular Expressions (PCRE) is a library written in C, which implements a regular expression engine, inspired by the capabilities of the...
extensively studied from various perspectives: extrinsically, relating to their embedding in Euclidean space and intrinsically, reflecting their properties determined...
polygons. p. 110 Deza, Michael; Shtogrin, Mikhael (1998). "Embedding the graphs of regular tilings and star-honeycombs into the graphs of hypercubes and...
surface embedding. Unlike the usual dual graph (which is an embedding of a generally different graph in the same surface) the Petrie dual is an embedding of...
five-dimensional projective space, and is realized by the Veronese embedding, the embedding of the projective plane given by the complete linear system of...
completely regular spaces are kinds of topological spaces. These conditions are examples of separation axioms. A Tychonoff space is any completely regular space...
R^{i}f'_{*}(g'^{*}{\mathcal {F}})} is an isomorphism. smooth algebra regularembedding Formally smooth map J. S. Milne (2012). "Lectures on Étale Cohomology"...
graph theory, a mathematical discipline, a linkless embedding of an undirected graph is an embedding of the graph into three-dimensional Euclidean space...
footprint and is well-suited for embedding in applications which require high-performance and concurrency. As with most embedded database systems, HailDB is...
rectifying the tetrahedron). The above embedding divides the cube into five tetrahedra, one of which is regular. In fact, five is the minimum number of...
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