Plücker formulas
E291201
Plücker formulas are classical algebraic geometry relations that connect the degree and singularities of plane algebraic curves with the invariants of their dual curves.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Plücker formulas canonical | 2 |
Statements (40)
| Predicate | Object |
|---|---|
| instanceOf |
classical result in algebraic geometry
ⓘ
set of formulas in algebraic geometry ⓘ |
| appearsIn | classical textbooks on algebraic geometry ⓘ |
| appliesTo |
irreducible plane projective curves
ⓘ
plane algebraic curves ⓘ |
| associatedWith |
enumerative geometry
ⓘ
projective duality ⓘ |
| assumes | curve is reduced ⓘ |
| context | projective plane ⓘ |
| expresses | constraints on possible singularity configurations ⓘ |
| field | algebraic geometry ⓘ |
| generalizationOf | earlier results on plane curve singularities ⓘ |
| givesRelationBetween |
degree and class of a plane curve
ⓘ
degree of a curve and degree of its dual ⓘ singularities of a curve and invariants of its dual ⓘ |
| historicalPeriod | 19th century mathematics ⓘ |
| influenced |
development of classical projective geometry
ⓘ
later work on dual varieties and discriminants ⓘ |
| involves |
class of a plane curve
ⓘ
class of the dual curve ⓘ degree of the dual curve ⓘ dual curve of a plane curve ⓘ number of cusps of a plane curve ⓘ number of nodes of a plane curve ⓘ |
| mathematicalDomain |
complex algebraic curves
ⓘ
projective algebraic curves ⓘ |
| namedAfter | Julius Plücker ⓘ |
| relatedConcept |
Severi varieties
ⓘ
adjunction formula ⓘ dual variety ⓘ genus of a plane curve ⓘ |
| relates |
degree of a plane curve
ⓘ
invariants of the dual curve ⓘ singularities of a plane curve ⓘ |
| requires |
classification of plane curve singularities into nodes and cusps
ⓘ
intersection theory in the projective plane ⓘ notions of multiplicity of intersection ⓘ |
| usedFor |
classifying plane algebraic curves
ⓘ
computing invariants of dual curves ⓘ studying singularities of plane curves ⓘ |
Referenced by (2)
Full triples — surface form annotated when it differs from this entity's canonical label.