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Intersection number

In mathematics, and especially in algebraic geometry, the intersection number generalizes the intuitive notion of counting the number of times two curves intersect to higher dimensions, multiple (more than 2) curves, and accounting properly for tangency. One needs a definition of intersection number in order to state results like Bézout's theorem.

Applications, Serre's Tor formula & Snapper–Kleiman definition of intersection number

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Serre's Tor formula

NonsingularProjective varietyFinite setProjective lineProjective plane
19 related topics

Snapper–Kleiman definition of intersection number

Euler characteristicPicard groupGrothendieck groupCoherent sheavesProper
9 related topics

Definition for Riemann surfaces

Riemann surfaceDifferential formPoincaré dualWedge productHodge star
8 related topics

Applications

Fixed pointsGraphsDiagonalsLefschetz fixed-point theorem
4 related topics

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Overview

Definition for Riemann surfaces

Definition for algebraic varieties

Serre's Tor formula

Further definitions

Snapper–Kleiman definition of intersection number

Intersection multiplicities for plane curves

Self-intersections

Applications

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Map overview Semantic statistics

Intersection number

Nodes69
Edges68
Triples40
Avg. degree1.97
Density0.028986
Components1

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Intersection number

Top relations

related to Snapper–Kleiman definition of intersection number · 10
Intersection number → Artinian, Cartier, Euler, Grothendieck, Kleiman, Let, Pic, Picard, Snapper, There
related to Serre's Tor formula · 9
Intersection number → First, If, In, Jean-Pierre Serre, Let, On, The, Then, This
related to Definition for Riemann surfaces · 6
Intersection number → For, Hodge, Let, Poincaré, Riemann, Then
has application · 4
Intersection number → Bézout's, Calculating, Lefschetz, The
related to Definition for algebraic varieties · 4
Intersection number → Specifically, The, Z1, Zn
related to Further definitions · 4
Intersection number → In, Poincaré, Specifically, The
related to Self-intersections · 3
Intersection number → In, Some, This

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Important terminology

intersection displaystyle number curves multiplicity two definition one algebraic divisors plane point isbn example position points dimension line nonsingular closed

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Intersection numberhas applicationThe0.60section
Intersection numberhas applicationBézout's0.60section
Intersection numberhas applicationCalculating0.60section
Intersection numberhas applicationLefschetz0.60section
Intersection numberrelated to Definition for algebraic varietiesThe0.60section
Intersection numberrelated to Definition for algebraic varietiesSpecifically0.60section
Intersection numberrelated to Definition for algebraic varietiesZ10.60section
Intersection numberrelated to Definition for algebraic varietiesZn0.60section
Intersection numberrelated to Definition for Riemann surfacesLet0.60section
Intersection numberrelated to Definition for Riemann surfacesRiemann0.60section
Intersection numberrelated to Definition for Riemann surfacesThen0.60section
Intersection numberrelated to Definition for Riemann surfacesFor0.60section

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