In mathematics, an algebraic variety V in projective space is a complete intersection if the ideal of V is generated by exactly codim V elements. That...

algebra, a complete intersection ring is a commutative ring similar to the coordinate rings of varieties that are complete intersections. Informally...

scheme, then B is a complete intersection ring. The notion is used, for instance, in an essential way in Fulton's approach to intersection theory. The important...

Any regular local ring is a complete intersection ring, but not conversely. A ring R is a set-theoretic complete intersection if the reduced ring associated...

smoothable complete intersection morphism, this complex is perfect. Furthermore, if g : Y → Z is another smoothable complete intersection morphism and...

In set theory, the intersection of two sets A {\displaystyle A} and B , {\displaystyle B,} denoted by A ∩ B , {\displaystyle A\cap B,} is the set containing...

) {\displaystyle {\mathcal {O}}_{X}(-n{-}1{+}d)} . For a smooth complete intersection i : X ↪ P S n {\displaystyle i:X\hookrightarrow \mathbb {P} _{S}^{n}}...

sense. This is the algebraic analogue of the geometric notion of a complete intersection. Given a commutative ring R and an R-module M, an element r in R...

hypersurfaces, one after the other. A projective algebraic set is a complete intersection if its defining ideal is generated by a regular sequence. In this...

Universally catenary rings ⊃ Cohen–Macaulay rings ⊃ Gorenstein rings ⊃ complete intersection rings ⊃ regular local rings For a commutative Noetherian local ring...

Diagonal intersection is a term used in mathematics, especially in set theory. If δ {\displaystyle \displaystyle \delta } is an ordinal number and ⟨ X...

projective variety that is not linear or a hypersurface, in fact not a complete intersection. It is the three-dimensional case of the rational normal curve,...

\mathbb {Z} /2\to 0} Consider a smooth complete intersection 3-fold X {\displaystyle X} (such as a complete intersection Calabi-Yau 3-fold). If we look at...

Universally catenary rings ⊃ Cohen–Macaulay rings ⊃ Gorenstein rings ⊃ complete intersection rings ⊃ regular local rings A Gorenstein ring is a commutative Noetherian...

An overview of Calabi-Yau Elliptic fibrations Lectures on the Calabi-Yau Landscape Fibrations in CICY Threefolds - (complete intersection Calabi-Yau)...

complete intersections of algebraic hypersurfaces whose sum of degrees is at most the total dimension of the ambient projective space. Such complete intersections...

an intersection graph is a graph that represents the pattern of intersections of a family of sets. Any graph can be represented as an intersection graph...

A protected intersection or protected junction, also known as a Dutch-style junction, is a type of at-grade road junction in which cyclists and pedestrians...

Cantor's intersection theorem, also called Cantor's nested intervals theorem, refers to two closely related theorems in general topology and real analysis...

algebraic geometry, the problem of residual intersection asks the following: Given a subset Z in the intersection ⋂ i = 1 r X i {\displaystyle \bigcap _{i=1}^{r}X_{i}}...

Universally catenary rings ⊃ Cohen–Macaulay rings ⊃ Gorenstein rings ⊃ complete intersection rings ⊃ regular local rings There are a number of useful definitions...

_{X}\cong {\mathcal {Ext}}_{O_{Y}}^{r}(O_{X},K_{Y}).} When X is a local complete intersection of codimension r in a smooth scheme Y, there is a more elementary...

An intersection or an at-grade junction is a junction where two or more roads converge, diverge, meet or cross at the same height, as opposed to an interchange...

In mathematics, and especially in algebraic geometry, the intersection number generalizes the intuitive notion of counting the number of times two curves...

The Dimensionally Extended 9-Intersection Model (DE-9IM) is a topological model and a standard used to describe the spatial relations of two regions (two...

traffic only, above the main conventional roadway intersection. It is known as the Hovenring. Complete streets Direction of traffic History of road transport...

NP-complete problems are the hardest of the problems to which solutions can be verified quickly. Somewhat more precisely, a problem is NP-complete when:...

Intersection is a smart cities technology and out-of-home advertising company. It was formed as a result of a merger between Control Group and Titan in...

vehicles behind a completed turn into the crossroad without any conflict to oncoming traffic. On the crossroad, the four-leg intersection is replaced by...

Intersection daylighting, or simply daylighting, is an urban design strategy to enhance safety at intersections by improving visibility. About 40-60%...