Research any topic before you write.

Find related topics. | Discover entities. | See connections. | Build a topical map.

Regular embedding: Local complete intersection morphisms and virtual tangent bundles, Examples and usage & Non-Noetherian case

In algebraic geometry, a closed immersion i : X ↪ Y {\displaystyle i:X\hookrightarrow Y} 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 X ∩ U {\displaystyle X\cap U} is generated by a regular sequence of length r. A regular embedding of codimension one is precisely an…

Language: English [EN]

Use the mouse wheel or two fingers (on touchscreens) to zoom in and out of the map.

Map view:

Zoom: 100%

More settings

Connection length 100% Label size 100% Node size 100% Line width 100% Label width 100%

Export map as:

Regular embedding topic overview

The analysis highlights Local complete intersection morphisms and virtual tangent bundles, Examples and usage and Non-Noetherian case as prominent areas in the source structure around Regular embedding.

Related topics: 22
Source areas: 4
Connected nodes: 26
Extracted relationships: 24
Concept neighborhoods: 16
Bridge connections: 26

What this topic covers Research coverage

Source areas are shown by the number of related topics found in each part of the analysis. Use smaller areas too: they can reveal specialized angles and content gaps.

Local complete intersection morphisms and virtual tangent bundles · 8 topics

Examples and usage · 6 topics

Non-Noetherian case · 4 topics

Overview · 4 topics

Smaller areas are not necessarily less important. They contain fewer connections in this analysis and can be useful for finding specialized angles or coverage gaps.

Suggested research paths

A focused starting point derived from the topic graph, ranked independently of the source article order.

Start with these areas

Explore all related topics Closing gaps

Browse the complete topic structure, not only the most central items. Less prominent entities and concepts can reveal missing angles, specialized context and useful research gaps. Each item opens a new analysis centered on that subject.

Overview

Examples and usage

Smooth Smooth morphism
Regular scheme
Complete intersection ring
Intersection theory
Normal sheaf
Normal cone Normal cone (algebraic geometry)

Local complete intersection morphisms and virtual tangent bundles

Smooth varieties Smooth variety
Graph morphism Graph morphism (algebraic geometry)
Flat morphisms Flat morphism
Grothendieck group
Locally free Locally free sheaf
Cotangent complex
Perfect Perfect complex
Grothendieck–Riemann–Roch theorem

Non-Noetherian case

SGA 6 Exposé VII Séminaire de géométrie algébrique du Bois Marie
Projective module
Koszul complex
Acyclic Acyclic complex

Advanced semantic analysis

Deeper signals for content research, entity SEO and topical coverage. The plain-language headings explain what each technical view is useful for.

How Regular embedding connects Entity context

The extracted context around Regular embedding shows recurring relationship patterns in the source. For example, Regular embedding → For, Fulton's, I/I, If Spec, In, S-morphism, Spec, Sym, The Another extracted example is Regular embedding → A-linear, A-module, Exposé VII, First, Koszul, Koszul-regular, Noetherian, SGA, Then. Use these groups to spot repeated connection types before inspecting the individual relationships.

Regular embedding

Top relations

related to Examples and usage · 9

Regular embedding → For, Fulton's, I/I, If Spec, In, S-morphism, Spec, Sym, The

related to Non-Noetherian case · 9

Regular embedding → A-linear, A-module, Exposé VII, First, Koszul, Koszul-regular, Noetherian, SGA, Then

related to Local complete intersection morphisms and virtual tangent bundles · 6

Regular embedding → EGA IV, For, Grothendieck, Let, Notice, Then

Important terminology

Use these terms to understand the vocabulary surrounding the topic, not as a checklist for keyword stuffing.

Important terminology

displaystyle regular embedding intersection smooth complete one isbn morphism hookrightarrow schemes ideal local scheme locally grothendieck de mathematics point codimension

Regular embedding relationships Subject–Predicate–Object triples

TTTA extracted 24 structured relationships around Regular embedding. Examples in this analysis include Regular embedding → related to Examples and usage → For and Regular embedding → related to Examples and usage → S-morphism. The table shows each extracted connection, where it came from and its confidence.

Subject	Predicate	Object	Confidence	Src
Regular embedding	related to Examples and usage	For	0.60	section
Regular embedding	related to Examples and usage	S-morphism	0.60	section
Regular embedding	related to Examples and usage	In	0.60	section
Regular embedding	related to Examples and usage	If Spec	0.60	section
Regular embedding	related to Examples and usage	Spec	0.60	section
Regular embedding	related to Examples and usage	The	0.60	section
Regular embedding	related to Examples and usage	Fulton's	0.60	section
Regular embedding	related to Examples and usage	I/I	0.60	section
Regular embedding	related to Examples and usage	Sym	0.60	section
Regular embedding	related to Local complete intersection morphisms and virtual tangent bundles	For	0.60	section
Regular embedding	related to Local complete intersection morphisms and virtual tangent bundles	Notice	0.60	section
Regular embedding	related to Local complete intersection morphisms and virtual tangent bundles	EGA IV	0.60	section

Related concept clusters Concept neighborhoods

The concept neighborhoods around Regular embedding bring nearby vocabulary together. In this analysis, examples include Regular, Smooth and Complete. Use the clusters to find adjacent concepts and terminology that may deserve separate research.

Regular embedding
- Regular
- Smooth
- Complete
- Hookrightarrow
- Given
- Intersection
- Point
- Ideal
- Local
- Morphism
- One
- Called
regular embedding
- Regular
- Smooth
- Point
- Complete
- Hookrightarrow
- Ideal
- Given
- Intersection
- Morphism
- Local
- One
- Called
regular sequence
- Smooth
- Complete
- Given
- Intersection
- Point
- Ideal
- Local
- Morphism
- One
- Called
- Free
- Map
regular scheme
- Smooth
- Complete
- Given
- Intersection
- Point
- Ideal
- Local
- Morphism
- One
- Called
- Free
- Map
smooth
- Morphism
- Embedding
- Regular
- Complete
- Example
- Intersection
- Displaystyle
- Local
- Called
- Finite
- Free
- Given
complete intersection ring
- Intersection
- Local
- Morphism
- Theory
- Smooth
- Example
- Morphisms
- Regular
- Displaystyle
- Scheme
- Used
- Embedding
smooth varieties
- Morphism
- Embedding
- Regular
- Complete
- Example
- Intersection
- Displaystyle
- Local
- Called
- Finite
- Free
- Given
local complete intersection morphisms and virtual tangent bundles
- Intersection
- Local
- Iv
- Morphisms
- Morphism
- Theory
- One
- Smooth
- Example
- Regular
- Displaystyle
- Scheme

Connections between topic areas Semantic bridges

For Regular embedding, one of the stronger structural bridges in this analysis connects Regular embedding with Local complete intersection morphisms and virtual tangent bundles. Bridges highlight paths between different parts of the map and can reveal research angles that are easy to miss in a flat list.

Min side: 3

Regular embedding — Local complete intersection morphisms and virtual tangent bundles · splits 18 ⟂ 9

Regular embedding — Examples and usage · splits 20 ⟂ 7

Regular embedding — Overview · splits 22 ⟂ 5

Regular embedding — Non-Noetherian case · splits 22 ⟂ 5

Map overview Semantic statistics

Regular embedding

Nodes27

Edges26

Triples24

Avg. degree1.93

Density0.074074

Components1

Source & methodology

TTTA analyzes the structure around Regular embedding to surface related topics, entities, relationships, concept neighborhoods and bridge connections. Use the map to explore areas such as Local complete intersection morphisms and virtual tangent bundles, Examples and usage & Non-Noetherian case, including less central topics that may reveal useful research gaps. Automatically extracted connections are research leads rather than rewritten encyclopedia content.

Source: Wikipedia — Regular embedding · EN edition · Analysis: TopicsToTalkAbout

For writers, content strategists, SEOs, marketers and creators — from quick topic research to advanced semantic analysis.

Regular embedding topic overview

What this topic covers Research coverage

Key facts & relationships

Suggested research paths

Start with these areas

Local complete intersection morphisms and virtual tangent bundles

Examples and usage

Non-Noetherian case

Explore all related topics Closing gaps

Overview

Examples and usage

Local complete intersection morphisms and virtual tangent bundles

Non-Noetherian case

Advanced semantic analysis

How Regular embedding connects Entity context

Regular embedding

Top relations

Important terminology

Important terminology

Regular embedding relationships Subject–Predicate–Object triples

Related concept clusters Concept neighborhoods

Connections between topic areas Semantic bridges

Map overview Semantic statistics

Regular embedding

Source & methodology